Pre-Calc

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

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asked by Chris
  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

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    posted by Reiny
  2. Thank you so much, this was very helpful :)

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    posted by Chris

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