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 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.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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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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