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    If f'(a)=0, and 0<f''(a), the f has a minimum at a. How do I go on proving this
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    Not an A Level maths student, but surely it would be a maximum point if the change in gradient is less than 0
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    (Original post by LikeClockwork)
    If f'(a)=0, and 0>f''(a), the f has a minimum at a. How do I go on proving this
    I'm assuming you mean "maximum" or your inequality symbol is the wrong way round?

    What level of maths are you at? A full university level proof of this is very different to a simple A Level argument.
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    (Original post by BobBobson)
    Not an A Level maths student, but surely it would be a maximum point if the change in gradient is less than 0
    If f'' is positive at a, I meant.
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    (Original post by LikeClockwork)
    If f'' is positive at a, I meant.
    For a basic proof, couldn't you work out the gradient at f(a+x) and f(a-x) in relation to the gradient at f(a), where x is a positive number. And then from that work out the positions of f(a+x) and f(a-x)

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    (Original post by BobBobson)
    For a basic proof, couldn't you work out the gradient at f(a+x) and f(a-x) in relation to the gradient at f(a), where x is a positive number. And then from that work out the positions of f(a+x) and f(a-x)

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    Don't worry I've already proved it
 
 
 
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