Find the absolute extrema of the function on the closed interval. y = 4 cos x, [0, 27] Step 1 The absolute extrema of a function on a closed interval will occur at any critical numbers in the interval or at the endpoints of that interval. Begin by differentiating the function with respect to x to identify any critical numbers. y = 4 cos x -4 sin (x) y' = -4 sin(r) To find the critical numbers of y, we find all x-values for which y' = and all x-values for which y' does not exist does not exist Step 2 The derivative exists for all values of x. We therefore find all x-values for which y = 0. Since y = -4 sin x, we need to solve -4 sin x =0 Step 3 In the interval (0, 27), -4 sin x = 0 at x = TI Thus, the critical number is x = Step 4 Evaluate y = 4 cos x at the critical number and at the interval endpoints, 0 and 2n. Left Critical Number Right Endpoint Endpoint y(0) = 4 Y() = y(27) =

Find the absolute extrema of the function on the closed interval. y = 4 cos x, [0, 27] Step 1 The absolute extrema of a function on a closed interval will occur at any critical numbers in the interval or at the endpoints of that interval. Begin by differentiating the function with respect to x to identify any critical numbers. y = 4 cos x -4 sin (x) y' = -4 sin(r) To find the critical numbers of y, we find all x-values for which y' = and all x-values for which y' does not exist does not exist Step 2 The derivative exists for all values of x. We therefore find all x-values for which y = 0. Since y = -4 sin x, we need to solve -4 sin x =0 Step 3 In the interval (0, 27), -4 sin x = 0 at x = TI Thus, the critical number is x = Step 4 Evaluate y = 4 cos x at the critical number and at the interval endpoints, 0 and 2n. Left Critical Number Right Endpoint Endpoint y(0) = 4 Y() = y(27) =

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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