Question

Can points of inflection be extrema?

Answer 1

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

My answer to your question is yes, an inflection point could be an extremum; 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 and a local (also global) minimum.