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Math Help - derivative relation query

  1. #1
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    derivative relation query

    Question is if f(x) is a differentiable function. If f'(c)=0 then f(x) has a local maximum or minimum at x=c. True of False?

    I would have thought this was true but answer in text states otherwise.

    Could someone clarify and explain please.
    Thanks
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  2. #2
    Junior Member toraj58's Avatar
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    it is not true. in fact c is a Critical Point:

    consider the graph of this function:

    <br />
f(x) = x^3<br />

    then

    <br />
f^{\prime} (x) = 3x^2<br />

    and

    f^{\prime} (0) = 0

    but x=0 is not neither min nor max it is inflection point where the concavity of the graph will be diversed.
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  3. #3
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    Let f(x)=x^3. What is the derivative of f evaluated at x=0? What happens to f at x=0?
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  4. #4
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    Thanks guys, makes perfect sense. Think I must be a little
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