Calculus Problem, Estimate h'(-1)

[bobraymund]

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) = e^f(x), estimate h'(-1).


2. The attempt at a solution

a)
h'(x) = f'(x)e^f(x)
h'(-1) = f'(-1)e^f(-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 :)

 

[lanedance]

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

 

[bobraymund]

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

 

[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...

 

[lanedance]

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