In marginal analysis, we use the estimate: f'(x) × f(x+1) – f(x) Usually, this estimate is pretty good. This exercise shows that sometimes it is not. Let f (x) = e". From HW 07, recall that f'(x) = e". For an arbitary a compare f'(x) and f(x+1)– f(x) by computing the ratio: f(r+1) – f(x) f'(x) What does this say about using the derivative f'(x) to estimate f(x+1) - f(x)?

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 In marginal analysis, we use the estimate:
f'(x) ~ f(x+1) - f(x)
Usually, this estimate is pretty good. This exercise shows that sometimes it is not. Let f(x) = e*. From
HW 07, recall that f'(x) = e". For an arbitary x compare f'(x) and f(x+1) – f(x) by computing the ratio:
%3D
f (x +1) – f(x)
f'(x)
What does this say about using the derivative f'(x) to estimate f(x+1) – f(x)?
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Transcribed Image Text:A In marginal analysis, we use the estimate: f'(x) ~ f(x+1) - f(x) Usually, this estimate is pretty good. This exercise shows that sometimes it is not. Let f(x) = e*. From HW 07, recall that f'(x) = e". For an arbitary x compare f'(x) and f(x+1) – f(x) by computing the ratio: %3D f (x +1) – f(x) f'(x) What does this say about using the derivative f'(x) to estimate f(x+1) – f(x)? 7:01 PM ENG e Type here to search 4/27/2021 *3 F10 247 F12 Home End Delete ock F3 F5 F9 F11 losert 24 4 Backspace 3 6 80 19 ,R T Y P S D F G K L H Z X C V N M Alt Alt PrtSc Ctri PgUp LU
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