b. By choosing a small enough value for h, you can estimate f' (a) with arbitrary precision by computing the lower bound, f(a – h) – f(a) , and the upper bound, f(a + h) – f(a) and interpolating (finding the average of the two bounds). To save -h h time, observe that the average of the lower and upper bounds is f(a + h) – f(a – h) 2h Use the method described with h = 0.000001 to estimate f'(0) to four decimal places. Give your answer using decimal notation.

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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Solve Part B (all the stuff in red boxes)

b. By choosing a small enough value for h, you can estimate f' (a) with arbitrary precision by computing the lower bound,
f(a – h) – f(a)
, and the upper bound,
f(a + h) – f(a) and interpolating (finding the average of the two bounds). To save
-h
h
time, observe that the average of the lower and upper bounds is
f(a + h) – f(a – h)
2h
Use the method described with h = 0.000001 to estimate f'(0) to four decimal places. Give your answer using decimal
notation.
Transcribed Image Text:b. By choosing a small enough value for h, you can estimate f' (a) with arbitrary precision by computing the lower bound, f(a – h) – f(a) , and the upper bound, f(a + h) – f(a) and interpolating (finding the average of the two bounds). To save -h h time, observe that the average of the lower and upper bounds is f(a + h) – f(a – h) 2h Use the method described with h = 0.000001 to estimate f'(0) to four decimal places. Give your answer using decimal notation.
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