Question

I have no idea how to do this problem. Any help would be greatly appreciated.
Consider the function f(x) for which f(0)=4 and f'(0)=11.
Find h'(0) for the function h(x)=1/(f(x)

Answer 1

whats the function h(x) again ??

Answer 2

anyways, you'll need chain rule here, you know whats a chain rule ?

Answer 3

To be honest I know the formula but I don't know how to use is properly. My professor was gone the last 4 days and the person we had teaching was foreign and I couldn't understand him.

Answer 4

ok, tell me again what h(x) is ?

Answer 5

h(x)=1/f(x)

Answer 6

ok, tell me deribative of 1/x first ?

Answer 7

-1/x^2

Answer 8

ok, so using chain rule,
derivative of 1/ f(x) will be
-1/f(x)^2 * [f'(x)]
got this ?

Answer 9

So how do I use that to find h'(0)

Answer 10

that was h'(x) =-1/f(x)^2 * [f'(x)]
now just put x=0
and you have both, f(0) ans f'(0)

Answer 11

Oh I understand. Thank you very much for your help

Answer 12

what you got as answer ? just to verify...

Answer 13

-11/16

Answer 14

thats correct :)
welcome ^_^

Answer 15

you sir saved my life. Thanks again

Answer 16

your are welcomed anytime :)