According to me it should not always be the case as a linear function in x ha double derivative zero at every point but does not change concavity.

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1

‘According to me’. I’m going to find a way to put that in a paper.

– Mattos

2 days ago

2

Convexity changes iff the second derivative changes sign. Just to become zero it is not enough. Example: f(x)=x4f(x)=x^4.

– A.G.

2 days ago

What about f(x)=0f(x) = 0?

– Ilya

2 days ago

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