# Calculus Problem, Estimate h'(-1)

1. Aug 28, 2010

### bobraymund

1. The problem statement, all variables and given/known data
A function f with domain [-5, 5] has a derivative f' whose graph is shown http://img718.imageshack.us/img718/2842/calcpic.jpg" [Broken]. 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 :)

Last edited by a moderator: May 4, 2017
2. Aug 28, 2010

### lanedance

doesn't f'(-1) = 3 from that picture?

3. Aug 28, 2010

### bobraymund

Hahaha, oh my gosh I'm stupid. Thank you. :P

4. Aug 28, 2010

### bobraymund

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...

5. Aug 28, 2010

### lanedance

so if you caclulate the derivtive of g(x) is negative, then that is sufficient to explain it is decreasing