Please solve and show work Applying the First Derivative Test InExercises 21-56, (a) find the critical numbersof f (if any), (b) find the open interval(s) onwhich the function is increasing or decreasing,and (c) apply the First Derivative Test to findall relative extrema. Use a graphing utility toconfirm your results.32. f(x) = x²/3 - 4

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Answered: Applying the ative Exercises 21-56, (a)…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.4: Definition Of The Derivative

Problem 50E

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YOUR TURN Find the absolute extrema of the function f(x)=3x2/33x5/3 on the interval [0,8].
Heat Gain The following graphs show the typical heat gain, in BTU per hour per square foot, for windows one with plain glass and one that is triple glazed in Pittsburgh in June, one facing east and one facing south. The horizontal axis gives the time of the day. Estimate the total heat gain per square foot by summing the areas of rectangle. Use rectangles with widths of 2hours, and let the function value at the midpoint of the subinterval give the height of rectangle. Source: Sustainable by Design. a. Estimate the total heat gain per square foot for a plain glass window facing east. b. Estimate the total heat gain per square foot for a triple glazed window facing east.
Heat Gain The following graphs show the typical heat gain, in BTU per hour per square foot, for windows one with plain glass and one that is triple glazed in Pittsburgh in June, one facing east and one facing south. The horizontal axis gives the time of the day. Estimate the total heat gain per square foot by summing the areas of rectangle. Use rectangles with widths of 2hours, and let the function value at the midpoint of the subinterval give the height of rectangle. Source: Sustainable by Design. a. Estimate the total heat gain per square foot for a plain glass window facing south. b. Estimate the total heat gain per square foot for a triple glazed window facing south.

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Applying the ative Exercises 21-56, (a) find the critical numbers of f (if any), (b) find the open interval(s) on which the function is increasing or decreasing, and (c) apply the First Derivative Test to find all relative extrema. Use a graphing utility to confirm your results.