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Math Help - Compute the Difference Quotient

  1. #1
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    Compute the Difference Quotient

    For the function f(x)=3x^3-34x. Compute the difference quotient f(x+h)-f(x)/h , where h is not equal to 0
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  2. #2
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    Re: Compute the Difference Quotient

    So, what's the problem?
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  3. #3
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    Re: Compute the Difference Quotient

    Hello, spyder12!

    I bet you didn't "cube" correctly.


    \text{Given the function: }f(x)\:=\:3x^3-34x

    \text{Compute the difference quotient: }\:\frac{f(x+h)-f(x)}{h}\,\text{ where }h \ne 0.

    f(x+h) \;=\;3(x+h)^3 - 34(x+h)

    n . . . . . =\;3(x^3 + 3x^2h + 3xh^2 + h^3) - 34(x+h)

    n . . . . . =\;3x^3 + 9x^2h + 9xh^2 + 3h^3 - 34x - 34h


    f(x+h) - f(x) \;=\;(3x^3 + 9x^2h + 9xh^2 + 3h^3 - 34x - 34h) - (3x^3 - 34x)

    n . . . . . . . . . . =\;9x^2h + 9xh^2 + 3h^3 - 34h


    \frac{f(x+h)-f(x)}{h} \;=\;\frac{9x^2h + 9xh^2 + 3h^3 - 34h}{h}

    . . . . . . . . . . . . =\;\frac{h\,(9x^2 + 9xh + 3h^2 - 34)}{h}

    . . . . . . . . . . . . =\;9x^2 + 9xh + 3h^2 - 34
    Thanks from spyder12
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  4. #4
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    Re: Compute the Difference Quotient

    thank you! you bet right haha
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