Tutorial Exercise Find the absolute maximum and absolute minimum values of f on the given interval. f(t) 2 cos t+ sin 2t [0.5] Part 1 of 5 To find the absolute maximum and minimum for f(t) = 2 cos t+ sin 2t on the interval [0, 1/2], we must find the largest and smallest function values at the critical numbers and at the interval endpoints. First, we'll find f'(t) = (No Response) -2 sin t+ (No Response) 2 cos 2t. Part 2 of 5 Since cos 2t = 1- 2 sin² t, then f'(t)= -2 sin t + 2 cos 2t = -2(2 sin² t + sin t-1), which simplifies to f'(t) = -2( Part 3 of 5 x 2 sin (t) 1) (sin t + 2x1 1). We have 0 = f'(t) = -2(2 sin t - 1) (sin t+1) when 0-2 sin t - 1, which means t = is not in the interval. is a critical number in the interval, or when 0= sin t + 1. However, the only value of t between 0 and 2x where this is true is at t = which
Tutorial Exercise Find the absolute maximum and absolute minimum values of f on the given interval. f(t) 2 cos t+ sin 2t [0.5] Part 1 of 5 To find the absolute maximum and minimum for f(t) = 2 cos t+ sin 2t on the interval [0, 1/2], we must find the largest and smallest function values at the critical numbers and at the interval endpoints. First, we'll find f'(t) = (No Response) -2 sin t+ (No Response) 2 cos 2t. Part 2 of 5 Since cos 2t = 1- 2 sin² t, then f'(t)= -2 sin t + 2 cos 2t = -2(2 sin² t + sin t-1), which simplifies to f'(t) = -2( Part 3 of 5 x 2 sin (t) 1) (sin t + 2x1 1). We have 0 = f'(t) = -2(2 sin t - 1) (sin t+1) when 0-2 sin t - 1, which means t = is not in the interval. is a critical number in the interval, or when 0= sin t + 1. However, the only value of t between 0 and 2x where this is true is at t = which
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.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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