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Math Help - If f ' (a) = 0, is always true that...

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    Senior Member sakonpure6's Avatar
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    If f ' (a) = 0, is always true that...

    If f'(a)=0, then there will always be a local extreme at x=a. Is this statement true or false. Explain and if it is false give a counter example.
    I say this is true because for f'(a)=0 that means that on f(x), x=a represent a point where mtangent=0 , representing a local extreme.
    Am I correct?

    Thanks!
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    MHF Contributor

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    Re: If f ' (a) = 0, is always true that...

    Quote Originally Posted by sakonpure6 View Post
    I say this is true because for f'(a)=0 that means that on f(x), x=a represent a point where mtangent=0 , representing a local extreme.
    You really need to carefully think about the function $f(x)=x^3$ at $x=0$.
    Thanks from sakonpure6 and HallsofIvy
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