Do points of inflection have to be differentiable?

1 Answer
Sep 20, 2014

That is a good question! I had to revisit the definition in the Calculus book by Stewart, which states:

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My answer to your question is no, a function does not need to be differentiable at a point of inflection; for example, the piecewise defined function

f(x)={(x^2,if x<0), (sqrt{x},if x ge0):}

is concave upward on (-infty,0) and concave downward on (0,infty) and is continuous at x=0, so (0,0) is an inflection point but not differentiable there.