Question

Find f(a) where a is in the domain of f.
f(x) = -1/x^2

I got a few steps into it and failed :(
The equation she gave me to plug it into is
(f(a+h)-f(a))/h

Answer 1

It looks like you are finding the derivative by First Principles.

f(a+h) = -1/(a+h)^2
f(a) = -1/a^2

then (f(a+h)-f(a))/h
= [-1/(a+h)^2 - (-1/a^2)]/h
= [-a^2 + (a+h)^2]/[(a^2(a+h)^2](1/h)
= [-a^2 + a^2 + 2ah + h^2]/[(a^2(a+h)^2](1/h)
= h(2a+h)/[(a^2(a+h)^2](1/h)
= (2a+h)/[(a^2(a+h)^2]

Now I will assume that you are going to take the limit of that as h --> 0
Am I right?
If so, then
LIM (2a+h)/[(a^2(a+h)^2] as h --> 0
= LIM (2a)/[(a^2(a)^2]
= 2a/a^4
= 2/a^3

Answer 2

Thank you so much, this was very helpful :)