(a) Show that f(x) = 2x + cos x is one-to-one. (b) What is the value of f(1)? (c) Use the formula from Exercise 53(a) to find (f)(1).

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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I'm answering question 54 but it uses the information from question 53.
53. (a) Suppose f is a one-to-one differentiable function and i
inverse function fis also differentiable. Use implicit
-
differentiation to show that
1
(f)(x) =
%3D
f'(f"(x))
provided that the denominator is not 0.
(b) If f(4) = 5 and f'(4) = 5, find (f-)'(5).
54. (a) Show that f(x) = 2x + cos x is one-to-one.
(b) What is the value of f(1)?
(c) Use the formula from Exercise 53(a) to find (f)(1).
%3D
Transcribed Image Text:53. (a) Suppose f is a one-to-one differentiable function and i inverse function fis also differentiable. Use implicit - differentiation to show that 1 (f)(x) = %3D f'(f"(x)) provided that the denominator is not 0. (b) If f(4) = 5 and f'(4) = 5, find (f-)'(5). 54. (a) Show that f(x) = 2x + cos x is one-to-one. (b) What is the value of f(1)? (c) Use the formula from Exercise 53(a) to find (f)(1). %3D
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