Fresh C.

asked • 01/05/18# If f is a differentiable function, and f ''(c)= 0 , then f has an inflection point at x=c . true /false

If f is a differentiable function, and f ''(c)= 0 , then f has an inflection point at x=c . true /false

is there a theorem that proves or disproves this?

is there a counter example?

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Ashley H.

No, its false. what about a parabola? The second derivative is zero at the vertex but it doesn't change signs on either side.06/10/19