2024 Increase decrease interval calculator

... intervals of increase and decrease of a function f: Compute the derivative f ... functions on your calculator, you may as well use this procedure as any other.. Johnston county recent arrest

The confidence level refers to the long-term success rate of the method, that is, how often this type of interval will capture the parameter of interest. A specific confidence interval gives a range of plausible values for the parameter of interest. Let's look at a few examples that demonstrate how to interpret confidence levels and confidence ... Find Where Increasing/Decreasing f (x)=1/x. f (x) = 1 x f ( x) = 1 x. Graph the polynomial in order to determine the intervals over which it is increasing or decreasing. Decreasing on: (−∞,0),(0,∞) ( - ∞, 0), ( 0, ∞) Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with ...Identify the intervals when 𝒇 is increasing and decreasing. Include a justification statement. 1. Increasing: Decreasing: 2. Increasing: Decreasing: For each function, find the intervals where it is increasing and decreasing, and JUSTIFY your conclusion. Construct a sign chart to help you organize the information, but do not use a calculator. 3.Using the TI 84 to find intervals in which a function is increasing or decreasing using the derivative.Deceleration, or decrease in speed, can be calculated using multiple different formulas, depending on the available parameters. Some deceleration formulas include a = (v – u)/t, and a = (v^2 – u^2) / (2s).Increasing and decreasing intervals are intervals of real numbers where the real-valued functions are increasing and decreasing respectively. To determine the increasing and …Precalculus. Find Where Increasing/Decreasing y=x^3. y = x3 y = x 3. Graph the equation in order to determine the intervals over which it is increasing or decreasing. Increasing on: (−∞,0),(0,∞) ( - ∞, 0), ( 0, ∞) Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with ...Analyzing Your Graph. What is the minimum or maximum value of your function? What is the interval of increase? What is the interval of decrease? 𝜋.Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval. The average rate of change of an increasing function is positive, and the average rate of change of a decreasing function is negative. Figure 3 shows examples of increasing and decreasing intervals on a function.A function is increasing on an interval if whenever A function is strictly increasing on an interval if whenever A function is decreasing on an interval if whenever A ...Example 1. Let's find the intervals where f ( x) = x 3 + 3 x 2 − 9 x + 7 is increasing or decreasing. First, we differentiate f : Now we want to find the intervals where f ′ is positive or negative. f ′ intersects the x -axis when x = − 3 and x = 1 , so its sign must be constant in each of the following intervals: This page titled 4.3: Graphing Using Calculus - Intervals of Increase/Decrease, Concavity, and Inflection Points is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Gilbert Strang & Edwin “Jed” Herman via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit ...A function is increasing on an interval if whenever A function is strictly increasing on an interval if whenever A function is decreasing on an interval if whenever A ...Example 7: Finding the Intervals of Increase and Decrease of a Rational Function. Determine the intervals on which the function 𝑓 (𝑥) = 7 𝑥 𝑥 + 9 is increasing and where it is decreasing. Answer . To establish intervals of increase and decrease for a function, we can consider its derivative, 𝑓 ′ (𝑥). Calculus. Find Where Increasing/Decreasing Using Derivatives f (x)=x^3-3x^2. f (x) = x3 − 3x2 f ( x) = x 3 - 3 x 2. Find the first derivative. Tap for more steps... 3x2 − 6x 3 x 2 - 6 x. Set the first derivative equal to 0 0 then solve the equation 3x2 −6x = 0 3 x 2 - 6 x = 0.As the sample size $n$ increases, the length of the interval decreases. The moral of the story, then, is to select as large of a sample as you can afford. As the confidence level decreases, the length of the interval decreases. (Consider, for example, that for a 95% interval, $z=1.96$, whereas for a 90% interval, $z=1.645$.)Example 1. Let's find the intervals where f ( x) = x 3 + 3 x 2 − 9 x + 7 is increasing or decreasing. First, we differentiate f : Now we want to find the intervals where f ′ is positive or negative. f ′ intersects the x -axis when x = − 3 and x = 1 , so its sign must be constant in each of the following intervals: When they calculate a two-sided confidence interval, the upper side of the interval is 18.4. However, because the company only cares about the upper bound, they can calculate a one-sided confidence interval instead. The one-sided confidence interval shows that the upper bound for the amount of dissolved solids is even lower, 17.8 mg/L. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Intervals of Increase and decrease | DesmosTo find the average rate of change, we divide the change in the output value by the change in the input value. Average rate of change = Change in output Change in input = Δy Δx = y2 − y1 x2 − x1 = f(x2) − f(x1) x2 − x1. The Greek letter Δ (delta) signifies the change in a quantity; we read the ratio as “delta- y over delta- x ... The interval to check if is increasing or decreasing is . Step 5. Substitute any number, such as , from the interval in the derivative to check if the result is negative or positive. If the result is negative, the graph is decreasing on the interval.With sample proportion, the margin of error increases as the proportion gets closer to 50%, and decreases when the proportion is closer to 0% or 100% – as we ...This page titled 4.3: Graphing Using Calculus - Intervals of Increase/Decrease, Concavity, and Inflection Points is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Gilbert Strang & Edwin "Jed" Herman via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit ...Algebra 1 Course: Algebra 1 > Unit 8 Lesson 9: Intervals where a function is positive, negative, increasing, or decreasing Increasing, decreasing, positive or negative intervals Worked example: positive & negative intervals Positive and negative intervals Increasing and decreasing intervals Math > Algebra 1 > Functions >A function is increasing if, as you move left to right, your pencil if moving upwardA function is decreasing if, as you move left to right, your pencil is mo...Wacky Math with Mr D. 4.7. (1) $1.25. PDF. Students will determine the intervals of increase and decrease for the functions provided as well as graph the functions and determine the relative maximum and minimums. This worksheet packet comes with a homework page at the end with four functions where students will use their calculator to determine ...DO : Try to follow the process (above) to work this problem before looking at the solution below. Solution: f′(x) = 3x2 − 6x = 3x(x − 2) f ′ ( x) = 3 x 2 − 6 x = 3 x ( x − 2) Since f′ f ′ is always defined, the critical numbers occur only when f′ = 0 f ′ = 0, i.e., at c = 0 c = 0 and c = 2 c = 2. Our intervals are (−∞, 0 ...Example 7: Finding the Intervals of Increase and Decrease of a Rational Function. Determine the intervals on which the function 𝑓 (𝑥) = 7 𝑥 𝑥 + 9 is increasing and where it is decreasing. Answer . To establish intervals of increase and decrease for a function, we can consider its derivative, 𝑓 ′ (𝑥).Question: f(x) = (1 - x)e (a) Find the intervals of increase or decrease. क Interval of increase ) Interval of decrease (b) Find the intervals of concavity. (Enter NONE in any unused answer blanks.) CU ) CDC ) (c) Find the points of inflection.Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval. The average rate of change of an increasing function is positive, and the average rate of change of a decreasing function is negative. Figure 3 shows examples of increasing and decreasing intervals on a function.When they calculate a two-sided confidence interval, the upper side of the interval is 18.4. However, because the company only cares about the upper bound, they can calculate a one-sided confidence interval instead. The one-sided confidence interval shows that the upper bound for the amount of dissolved solids is even lower, 17.8 mg/L.Expert Answer. When we move left to right on x axis and function (y value) is increasing then it i …. View the full answer. Transcribed image text: Identify intervals of increase, decrease, or constant The function graphed above is: Increasing on the interval (s) Decreasing on the interval (s) Question Help: Message instructor.Calculus Find Where Increasing/Decreasing f (x) = square root of x f (x) = √x f ( x) = x Graph the polynomial in order to determine the intervals over which it is increasing or decreasing. Increasing on: (0,∞) ( 0, ∞)Use this calculator to determine a confidence interval for your odds ratio. ... Increasing the confidence level to 99% this interval would increase to between ...Lesson Plan. Students will be able to. recall the condition for a function to be increasing, decreasing, or constant over the interval ( 𝑎, 𝑏), identify the increasing and decreasing intervals of a simple function from its equation, identify the increasing and decreasing intervals of a function from its graph, give conditions for which a ...Substitute a value from the interval (5,∞) ( 5, ∞) into the derivative to determine if the function is increasing or decreasing. Tap for more steps... Increasing on (5,∞) ( 5, ∞) …Possible Answers: is increasing if, for any (i.e the slope is always greater than or equal to zero) Find the increasing intervals of the following function on the interval. derivative. To find these intervals, first find the critical values, or the points at which the first derivative of the function is equal to zero.Use this calculator to determine a confidence interval for your odds ratio. ... Increasing the confidence level to 99% this interval would increase to between ...Find the intervals of decrease or increase for the function x^2 - 9x + 7. Find the intervals of increase and decrease of the function: f(x) = \sqrt{18-7x-x^2} Find the interval where the function is increasing and the interval where it is decreasing. f(x) = 2x^2 + 2x + 8; Find the interval of increase or decrease for f(x) = x^3-7x^3+12x^2-7x+1.To find the average rate of change, we divide the change in the output value by the change in the input value. Average rate of change = Change in output Change in input = Δy Δx = y2 − y1 x2 − x1 = f(x2) − f(x1) x2 − x1. The Greek letter Δ (delta) signifies the change in a quantity; we read the ratio as “delta- y over delta- x ... To find the critical points of a two variable function, find the partial derivatives of the function with respect to x and y. Then, set the partial derivatives equal to zero and solve the system of equations to find the critical points. Use the second partial derivative test in order to classify these points as maxima, minima or saddle points.This is a short tutorial on using Desmos online graphing calculator to determine local extrema and intervals of increase and decrease of a function.Calculus. Find Where Increasing/Decreasing f (x) = cube root of x. f (x) = 3√x f ( x) = x 3. Graph the polynomial in order to determine the intervals over which it is increasing or decreasing. Increasing on: (−∞,0),(0,∞) ( - ∞, 0), ( 0, ∞) Free math problem solver answers your algebra, geometry, trigonometry, calculus, and ...Using the TI 84 to find intervals in which a function is increasing or decreasing using the derivative.I will present here a modified method based on the principle of a control chart and a calendar-time method as per ILAC G24 (OIML D 10:2007). I will call this method the ‘Floating Interval Method’ because it can increase or decrease in a given condition. To establish a fixed interval, below is the calibration interval analysis procedure: 1.Example 7: Finding the Intervals of Increase and Decrease of a Rational Function. Determine the intervals on which the function 𝑓 (𝑥) = 7 𝑥 𝑥 + 9 is increasing and where it is decreasing. Answer . To establish intervals of increase and decrease for a function, we can consider its derivative, 𝑓 ′ (𝑥).This is a short tutorial on using Desmos online graphing calculator to determine local extrema and intervals of increase and decrease of a function.I will present here a modified method based on the principle of a control chart and a calendar-time method as per ILAC G24 (OIML D 10:2007). I will call this method the ‘Floating Interval Method’ because it can increase or decrease in a given condition. To establish a fixed interval, below is the calibration interval analysis procedure: 1.Identify the intervals when 𝒇 is increasing and decreasing. Include a justification statement. 1. Increasing: Decreasing: 2. Increasing: Decreasing: For each function, find the intervals where it is increasing and decreasing, and JUSTIFY your conclusion. Construct a sign chart to help you organize the information, but do not use a calculator. 3.2. Rates of increase is a small part of quadratic functions but a very interesting and powerful one. Rates of increase is all about the change of one variable as the other increases. An easy way to see this is by making tables. In this example, we will look at a rock thrown up into the air with an initial velocity of 50m/s2.Given information about the probability of an outcome under control and experimental treatments, this calculator produces measures of risk increase/decrease and number needed to treat or harm, including confidence intervals. If some patients were lost to follow-up, the calculator provides estimates for several different scenarios. Dec 21, 2020 · Figure 3.3.1: A graph of a function f used to illustrate the concepts of increasing and decreasing. Even though we have not defined these terms mathematically, one likely answered that f is increasing when x > 1 and decreasing when x < 1. We formally define these terms here. Decrease the dosage interval to the next frequency . OR . Increase dose by 250-500 mg . 10-15 If goal is 10-15 mcg/mL No change If goal is 15-20 mcg/mL Increase dose by 250-500 mg . 15-20 If goal is 10-15 mcg/mL Decrease dose by 250-500 mg If goal is 15-20 mcg/mL No change . 20-25 . Decrease dose by 250-500 mg . OR . Increase the dosage ...WEBSITE: http://www.teachertube.com Finding Increasing Intervals with a Graphing Calculator... intervals of increase and decrease of a function f: Compute the derivative f ... functions on your calculator, you may as well use this procedure as any other.Step 3 -Test the points from all the intervals. We have got two zeroes or roots that are 1 and -1. These roots show that we have got three intervals that are , , and . We will take the value from each interval and see if it is increasing or decreasing. Lets take -2 from the interval and substitute it in the derivative of a function:Finishing a brain exercise for measuring a drug serum concentration (C), Prof. Brown starts to explain how to adapt the dose and dosing interval (tau). The changes in volume (V) and clearance (CL) are out of our control, but we can change the dose and dosing interval (tau) to optimize the drug use. There are four examples in this video, and the ...A function basically relates an input to an output, there’s an input, a relationship and an output. For every input... Read More. Save to Notebook! Sign in. Free functions extreme points calculator - find functions extreme and saddle points step-by-step. $\begingroup$ The notion of strictly increasing at a point is widely used in real analysis, and it means that left of the point you're lower and right of the point you're higher. This is a weaker notion that that of strictly increasing in some interval of the point, a notion that has less use in mathematics. I don't have time to say more now, but googling …Given information about the probability of an outcome under control and experimental treatments, this calculator produces measures of risk increase/decrease and number needed to treat or harm, including confidence intervals. If some patients were lost to follow-up, the calculator provides estimates for several different scenarios. ٠١‏/١٠‏/٢٠١٧ ... Using the TI-84 to find maximum and minimum values and using those values to find the intervals where the function is increasing and/or ...Calculus Find Where Increasing/Decreasing Using Derivatives f (x)=x^3-75x+3 f (x) = x3 − 75x + 3 f ( x) = x 3 - 75 x + 3 Find the first derivative. Tap for more steps... 3x2 − 75 3 x 2 - 75 Set the first derivative equal to 0 0 then solve the equation 3x2 −75 = 0 3 x 2 - 75 = 0. Tap for more steps... x = 5,−5 x = 5, - 5Then: divide the decrease by the original number and multiply the answer by 100. % Decrease = Decrease ÷ Original Number × 100. If your answer is a negative number, then this is a percentage increase. If you wish to calculate the percentage increase or decrease of several numbers then we recommend using the first formula. for one-variable real functions: limits, integrals, roots... This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, ...If the slope (or derivative) is positive, the function is increasing at that point. If it’s negative, the function is decreasing. So to find intervals of a function that are either decreasing or increasing, take the derivative and plug in a few values. Example Question: Find the increasing function intervals for g(x) = (&frac13;)x 3 + 2.5x 2 ...Jul 18, 2018 · A function is increasing on an interval if whenever A function is strictly increasing on an interval if whenever A function is decreasing on an interval if whenever A ... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Intervals of Increase and decrease | DesmosConsider a function f (x) = x 3 + 3x 2 - 45x + 9. To find intervals of increase and decrease, you need to differentiate them concerning x. After differentiating, you will get the first derivative as f' (x). Therefore, f' (x) = 3x 2 + 6x - 45Expert Answer. Transcribed image text: fx) - (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value (s). (Enter your answers as a comma- separated list.) Find the local maximum value (s).٢٨‏/٠٥‏/٢٠٢١ ... Find intervals of increase or decrease. F(x)=(5x)/(x^2 + 1). not supposed to use graphing calculator make use of number line I just don't know ...The music interval calculator helps you determine an interval between two notes. To find the interval between two pitches, choose from sounds in nine octaves and discover the simple and compound name for any distance greater than an octave. If you want to know an interval between notes, the calculator will differentiate between …Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Intervals of …Sample Size Calculator Terms: Confidence Interval & Confidence Level. The confidence interval (also called margin of error) is the plus-or-minus figure usually reported in newspaper or television opinion poll results. For example, if you use a confidence interval of 4 and 47% percent of your sample picks an answer you can be "sure" that if you had …The percentage increase calculator should be used as follows: Step 1: Enter the appropriate numbers in the respective input fields. Step 2: To obtain the percentage change, click the "Solve" option now. Step 3: Lastly, the output field will show the percentage increase (or decrease, depending on the input) for the specified value.Calculus Find Where Increasing/Decreasing Using Derivatives f (x)=x^3-75x+3 f (x) = x3 − 75x + 3 f ( x) = x 3 - 75 x + 3 Find the first derivative. Tap for more steps... 3x2 − 75 3 x 2 - 75 Set the first derivative equal to 0 0 then solve the equation 3x2 −75 = 0 3 x 2 - 75 = 0. Tap for more steps... x = 5,−5 x = 5, - 5A free online 2D graphing calculator (plotter), or curve calculator, that can plot piecewise, linear, quadratic, cubic, quartic, polynomial, trigonometric, hyperbolic, exponential, …Apr 29, 2023 · This confidence interval calculator is a tool that will help you find the confidence interval for a sample, provided you give the mean, standard deviation and sample size. You can use it with any arbitrary confidence level. If you want to know what exactly the confidence interval is and how to calculate it, or are looking for the 95% confidence ... Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step٢٥‏/٠٨‏/٢٠٢٣ ... Using a graphing calculator, estimate the interval on which the function is increasing or decreasing and any relative maxima or minima.1. So im supposed to find the interval of decrease and increase here. Ive gotten up to taking the derivative which is −4x(x2 − 1) − 4 x ( x 2 − 1) and then setting it to 0 i got ( …Calculus Find Where Increasing/Decreasing Using Derivatives f (x)=x^3-75x+3 f (x) = x3 − 75x + 3 f ( x) = x 3 - 75 x + 3 Find the first derivative. Tap for more steps... 3x2 − 75 3 x 2 - 75 Set the first derivative equal to 0 0 then solve the equation 3x2 −75 = 0 3 x 2 - 75 = 0. Tap for more steps... x = 5,−5 x = 5, - 5Free functions Monotone Intervals calculator - find functions monotone intervals step-by-stepFree Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepPolynomial graphing calculator. This page helps you explore polynomials with degrees up to 4. The roots (x-intercepts), signs, local maxima and minima, increasing and decreasing intervals, points of inflection, and concave up-and-down intervals can …The music interval calculator helps you determine an interval between two notes. To find the interval between two pitches, choose from sounds in nine octaves and discover the simple and compound name for any distance greater than an octave. If you want to know an interval between notes, the calculator will differentiate between …Intervals of Increase and Decrease. Find the first derivative test. We learn how to find the x-coordinates of all critical points, find all discontinuities...f ′ can only change sign at a critical number. The reason is simple. If f ′ ( x) is continuous and it changes sign, then it has to pass through 0 on its way from negative to positive (or vice versa ). That's the Intermediate Value Theorem. If f ′ ( x) is not continuous where it changes sign, then that is a point where f ′ ( x) doesn't ...

The confidence level refers to the long-term success rate of the method, that is, how often this type of interval will capture the parameter of interest. A specific confidence interval gives a range of plausible values for the parameter of interest. Let's look at a few examples that demonstrate how to interpret confidence levels and confidence .... My apps topgolf

Interval of Increasing Decreasing of a Functiongp104181937716343086902. Using the TI-84 to find maximum and minimum values and using those values to find the intervals where the function is increasing and/or decreasing.This page titled 4.3: Graphing Using Calculus - Intervals of Increase/Decrease, Concavity, and Inflection Points is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Gilbert Strang & Edwin “Jed” Herman via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit ... Expert Answer. When we move left to right on x axis and function (y value) is increasing then it i …. View the full answer. Transcribed image text: Identify intervals of increase, decrease, or constant The function graphed above is: Increasing on the interval (s) Decreasing on the interval (s) Question Help: Message instructor.2. Rates of increase is a small part of quadratic functions but a very interesting and powerful one. Rates of increase is all about the change of one variable as the other increases. An easy way to see this is by making tables. In this example, we will look at a rock thrown up into the air with an initial velocity of 50m/s2.Then: divide the decrease by the original number and multiply the answer by 100. % Decrease = Decrease ÷ Original Number × 100. If your answer is a negative number, then this is a percentage increase. If you wish to calculate the percentage increase or decrease of several numbers then we recommend using the first formula. $\begingroup$ The notion of strictly increasing at a point is widely used in real analysis, and it means that left of the point you're lower and right of the point you're higher. This is a weaker notion that that of strictly increasing in some interval of the point, a notion that has less use in mathematics. I don't have time to say more now, but googling …Students will learn how to determine where a function is increasing or decreasing and the corresponding notation for intervals. 1.3 Introduction to Increasing and Decreasing • Activity Builder by DesmosFigure 3.3.1: A graph of a function f used to illustrate the concepts of increasing and decreasing. Even though we have not defined these terms mathematically, one likely answered that f is increasing when x > 1 and decreasing when x < 1. We formally define these terms here.The relative risk calculator can be used to estimate the relative risk (or risk ratio) and its confidence interval for two different exposure groups. Enter the data into the table below, select the required confidence level from the dropdown menu, click "Calculate" and the results will be displayed below. Disease.The percentage change calculator is a web-based utility that offers assistance to users in the percentage change calculation between two values. It allows the users to find how much percentage increase or decrease has occurred in two numbers. The easy-to-use interface of our percent change calculator makes this task effortless for everyone.Symbolab is the best calculus calculator solving derivatives, integrals, limits, series, ODEs, and more. What is differential calculus? Differential calculus is a branch of calculus that includes the study of rates of change and slopes of functions and involves the concept of a derivative.The calculator will try to find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical (stationary) points, extrema (minimum and maximum, local, relative, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the singl... Example 1. Let's find the intervals where f ( x) = x 3 + 3 x 2 − 9 x + 7 is increasing or decreasing. First, we differentiate f : Now we want to find the intervals where f ′ is positive or negative. f ′ intersects the x -axis when x = − 3 and x = 1 , so its sign must be constant in each of the following intervals: The calculator will try to find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical (stationary) points, extrema (minimum and maximum, local, relative, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the singl...٢٩‏/١٠‏/٢٠١٩ ... Free Online Scientific Notation Calculator. Solve advanced ... when describing more thanTWO continuities, intervals of increase, decrease?Percentage increase/decrease calculation. The percentage increase/decrease from old value (V old) to new value (V new) is equal to the old and new values difference divided by the old value times 100%: percentage increase/decrease = (V new - V old) / V old × 100%. Example #1. Price percentage increase from old value of $1000 to new value of ... Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Increasing/Decreasing Intervals | Desmosis (c,f(c)). After locating the critical number(s), choose test values in each interval between these critical numbers, then calculate the derivatives at the test values to decide whether the function is increasing or decreasing in each given interval. (In general, identify values of the function which are discontinuous, so, in addition toThe intervals of increasing are (-1/6pi+2kpi, 7/6pi+2kpi) The intervals of decreasing are (7/6pi+2kpi, 11/6pi+2kpi), AA k in ZZ Calculate the first derivative y=x-2cosx dy/dx=1+2sinx The critical points are when dy/dx=0 1+2sinx=0 sinx=-1/2 x in (-1/6pi+2kpi) ... We build a sign chart in the interval # x in [-1/6pi, 19/6pi]# #color ....

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