Question

A non differentiable function can have point of inflection

Answer 1

A differentiable function has an inflection point at (x, f(x)) if and only if its first derivative, f′, has an isolated extremum at x. (This is not the same as saying that f has an extremum). ... If all extrema of f′ are isolated, then an inflection point is a point on the graph of f at which the tangent crosses the curve.