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Math Help - Find Average rate of change

  1. #1
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    Find Average rate of change

    f(x) = x^3 - 4x^2

    find the avergae rate of change for x = a and x = a + h
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  2. #2
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    is this correct?

    this is what i got:

    2a^3 + 2h^3 + h^3 + 2a^2h - 4a^2 / h
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  3. #3
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    Quote Originally Posted by needhelp75 View Post
    f(x) = x^3 - 4x^2

    find the avergae rate of change for x = a and x = a + h
    The average rate of change is given by \frac{f(a + h) - f(a)}{h}.


    f(a+h) = (a + h)^3 - 4(a + h)^2

     = a^3 + 3a^2h + 3ah^2 + h^3 - 4a^2 - 8ah -4h^2


    f(a) = a^3 - 4a^2


    f(a+h) - f(a) = 3a^2h + 3ah^2 + h^3 - 8ah - 4h^2


    \frac{f(a+h) - f(a)}{h} = 3a^2 + 3ah + h^2 - 8a - 4h.
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    thank you
    you = win + genius
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  5. #5
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    Quote Originally Posted by needhelp75 View Post
    thank you
    you = win + genius
    Thanks :P

    Before I teach calculus, I teach them the Binomial Theorem, so they can expand expressions like (a + h)^n.

    If it helps, Binomial theorem - Wikipedia, the free encyclopedia
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