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33-34 For what values of x does the graph of f have a horizontal tangent? Hercnt 33. f(x) = x + 2 sin x 34. f(x) = e* cos x

33-34 For what values of x does the graph of f have a horizontal tangent? Hercnt 33. f(x) = x + 2 sin x 34. f(x) = e* cos x

Calculus: Early Transcendentals
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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SECTION 3.3 DERIVATIVES OF TRIGONOMETRIC FUNCTIONS 197 29. If H(0) = 0 sin 6, find H'(0) and H"(0). O osot Sine 30. If f(t) = csc t, find f"(#/6). CsC x 31. (a) Use the Quotient Rule to differentiate the function 1. sec x (x)f (b) Simplify the expression for f(x) by writing it in terms of sin x and cos x, and then find f'(x). (c) Show that your answers to parts (a) and (b) are equivalent. bot (p 32. Suppose f(T/3) = 4 and f'(7/3) = -2, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find (a) g'(T/3) 38-48 (b) h'(/3) 38 33-34 For what values of x does the graph of f have a horizontal tangent? 15 niz 34. f(x) = e* cos x 33. f(x) = x + 2 sin x %3| 35. A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is n x(t) = 8 sin t, where t is in seconds and x in centimeters. (a) Find the velocity and acceleration at time t. (b) Find the position, velocity, and acceleration of the mass at time t = 2™/3. In what direction is it moving at that %3D time? equilibrium position ps bie 01
Transcribed Image Text:SECTION 3.3 DERIVATIVES OF TRIGONOMETRIC FUNCTIONS 197 29. If H(0) = 0 sin 6, find H'(0) and H"(0). O osot Sine 30. If f(t) = csc t, find f"(#/6). CsC x 31. (a) Use the Quotient Rule to differentiate the function 1. sec x (x)f (b) Simplify the expression for f(x) by writing it in terms of sin x and cos x, and then find f'(x). (c) Show that your answers to parts (a) and (b) are equivalent. bot (p 32. Suppose f(T/3) = 4 and f'(7/3) = -2, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find (a) g'(T/3) 38-48 (b) h'(/3) 38 33-34 For what values of x does the graph of f have a horizontal tangent? 15 niz 34. f(x) = e* cos x 33. f(x) = x + 2 sin x %3| 35. A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is n x(t) = 8 sin t, where t is in seconds and x in centimeters. (a) Find the velocity and acceleration at time t. (b) Find the position, velocity, and acceleration of the mass at time t = 2™/3. In what direction is it moving at that %3D time? equilibrium position ps bie 01
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