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Math Help - rate of change type

  1. #1
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    Unhappy rate of change type

    Let f(x) = root x. If the rate of change of f at x = c is twice its rate of change at x=1, then c=...?

    i have no idea what to do.
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  2. #2
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    Quote Originally Posted by abcocoa View Post
    Let f(x) = root x. If the rate of change of f at x = c is twice its rate of change at x=1, then c=...?
    i have no idea what to do.
    Hello,

    the rate of change is calculated by the first derivative:

    f'(x)=\frac{df}{dx}=\frac{1}{2 \sqrt{x}}

    Now calculate f'(1) = 1/2. That means you know now the value of the rate of change at c: It is 1. Therefore solve the following equation for c:

    f'(c)=\frac{1}{2 \sqrt{c}}=1. I've got  c=\frac{1}{4}

    EB
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