Can points of inflection be extrema?

1 Answer
Wataru
Sep 19, 2014

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

enter image source here

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.

Related questions
See all questions in Critical Points of Inflection
Impact of this question
14344 views around the world
You can reuse this answer
Creative Commons License