Calculus Problem, Estimate h'(-1)

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Homework Help Overview

The discussion revolves around estimating the derivative of the function h(x) = ef(x) at x = -1, given the derivative f' and the value of f(-1). Participants are analyzing the implications of the derivative's graph and its relationship to the function h.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the chain rule to find h'(-1) and questions the accuracy of their estimate for f'(-1) based on the provided graph. Another participant suggests a different value for f'(-1), prompting a reconsideration of the original estimate.

Discussion Status

Participants are actively engaging with the problem, with some offering corrections and others exploring the implications of their calculations. There is a recognition of differing interpretations regarding the value of f'(-1>, but no consensus has been reached on the correct estimate.

Contextual Notes

Participants are working with a graph that is not directly visible in the thread, which may affect their ability to accurately assess f'(-1). Additionally, there is a follow-up question regarding the behavior of another function g(x) based on its derivative, which introduces further complexity to the discussion.

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Homework Statement


A function f with domain [-5, 5] has a derivative f' whose graph is shown http://img718.imageshack.us/img718/2842/calcpic.jpg" . Also, f(-1) = 2.

a) If h(x) = ef(x), estimate h'(-1).


2. The attempt at a solution

a)
h'(x) = f'(x)ef(x)
h'(-1) = f'(-1)ef(-1)
= e2f'(-1)

f'(-1) = (2 - 3)/(0-(-1)) = -1/1 = -1

h'(-1) = -e2

Issues I'm having

So I'm not exactly sure if my estimate of f'(-1) is accurate based on the graph. What do you all think?

Thanks,
Bob :)
 
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doesn't f'(-1) = 3 from that picture?
 
Hahaha, oh my gosh I'm stupid. Thank you. :P
 
Another part of the question is:

Suppose that g(x) = 1/[f(x)]2. Is g(x) increasing when x = -1? Explain.

It would be decreasing, right? Because the derivative is -1/4. I don't get how to explain that...
 
so if you caclulate the derivtive of g(x) is negative, then that is sufficient to explain it is decreasing
 

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