(a) Suppose y = f(x) is an unknown function but that you know that f(4) = 11 and f'(4) = -0.18. Explain how you would estimate f(4.2), and then do it. Show all work. (b) Suppose that you also know f"(4) > 0. Does this suggest your answer to part a) is an over or under estimate? Explain. (Hint: draw a couple pictures as part of your thinking process.)

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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(a) Suppose y = f(x) is an unknown function but that you know that f(4) = 11 and
f'(4) = -0.18. Explain how you would estimate f(4.2), and then do it. Show all
work.
(b) Suppose that you also know f"(4) > 0. Does this suggest your answer to part a)
is an over or under estimate? Explain. (Hint: draw a couple pictures as part of
your thinking process.)
Transcribed Image Text:(a) Suppose y = f(x) is an unknown function but that you know that f(4) = 11 and f'(4) = -0.18. Explain how you would estimate f(4.2), and then do it. Show all work. (b) Suppose that you also know f"(4) > 0. Does this suggest your answer to part a) is an over or under estimate? Explain. (Hint: draw a couple pictures as part of your thinking process.)
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