Can points of inflection be extrema?

1 Answer
Sep 19, 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 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.