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Having Issues with Solving Derivatives

  1. Jul 21, 2013 #1
    1. The problem statement, all variables and given/known data
    Use the definition of a derivative to compute the derivative of the function at the given value.
    P(t)=t^3-4, t=-2


    2. Relevant equations
    Please help me solve it in this form: f(a+h)-f(a)/h
    lim
    h→0


    3. The attempt at a solution
    (-2+h)^3-(-2^3)-4/h=(h^3-6h^2+12h-4)/h=h^2-6h+8=0-0+8=8

    I am sick and tired of using the exact method the textbook gives me and getting answers that are miles off.
     
  2. jcsd
  3. Jul 21, 2013 #2

    lurflurf

    User Avatar
    Homework Helper

    first find
    P(t+h)-P(t)=((t+h)^3-4)-(t^3-4)

    (-2+h)^3-(-2^3)-4/h=(h^3-6h^2+12h-4)/h=h^2-6h+8=0-0+8=8
    should be
    ((-2+h)^3-4)-((-2^3)-4))/h=(h^3-?h^2+?h)/h=h^2-?h+?->0^2-?0+?=?
    where I have replaced numbers with ? for you to fill in
     
  4. Jul 21, 2013 #3
    Correct?
     
    Last edited: Jul 21, 2013
  5. Jul 22, 2013 #4

    Mark44

    Staff: Mentor

    Looks good.
     
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