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small maths proof help

If f'(a)=0, and 0<f''(a), the f has a minimum at a. How do I go on proving this
(edited 7 years ago)
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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Notnek
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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.
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.
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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