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Math Help - Solve 3

  1. #1
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    Solve 3

    Houw would I solve.
    Derivative formula (instantaneous rate of change formula for a function) find the derivative.

    a) f(x)=x^2-9x-10

    b) Check the answer by then finding the derivative of the same
    function above using the short-cut rules for finding derivatives.
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  2. #2
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    Quote Originally Posted by Hallah_az
    Houw would I solve.
    Derivative formula (instantaneous rate of change formula for a function) find the derivative.

    a) f(x)=x^2-9x-10

    b) Check the answer by then finding the derivative of the same
    function above using the short-cut rules for finding derivatives.
    a) The general formula (at least for Calc 1) for a derivative is:
    f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

    In this case
    f(x+h)=(x+h)^2-9(x+h)-10
    =x^2+2hx+h^2-9x-9h-10
    So:
    f(x+h)-f(x)=2hx+h^2-9h

    Thus
    f'(x)=\lim_{h \to 0}=\frac{2hx+h^2-9h}{h}=\lim_{h \to 0}(2x-9+h)=2x-9

    b) The power rule states that the derivative of  ax^n is nax^{n-1} and we know the derivative of a constant is zero, so the derivative of x^2-9x-10 is:
    2x^{2-1}-9x^{1-1}+0=2x^1-9x^0=2x-9.

    -Dan
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