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Why does d2y/dx^2 > 0 or < 0 tell the nature of a stationary point?

UKBrah

Any reasoning/proof?

Reply 1

TenOfThem

Original post by UKBrah

Any reasoning/proof?

It is the rate of change of gradient

At a minimum point the gradient changes from -ve before the point to 0 at the point to +ve after the point

So the gradient is increasing and has a +ve rate of change

Reply 2

steve2005

Original post by UKBrah

Any reasoning/proof?

Here is a graphical display of y=f(x), etc.

My computer has worked out all of these , normally of course the results would be simplified but I have left them in their raw state.