2
$\begingroup$

I often see these two terms being used (mainly in Calculus books) and I never know if they mean the same thing and can be used interchangeably or not. Does anyone know ?

$\endgroup$
  • $\begingroup$ The terms may be used interchangeably. Extrema refers to a location where the derivative is $0$ and 2nd derivative non-zero. Maximums and minimums are both types of extrema $\endgroup$ – infinitylord Nov 28 '16 at 15:53
  • 1
    $\begingroup$ There might be a few isolated exceptions, but in the vast majority of the books I've seen, "extrema" means "maximum or minimum". And "local extrema" means "local maximum or local minimum", "global extrema" means . . . $\endgroup$ – Dave L. Renfro Nov 28 '16 at 15:54
  • 1
    $\begingroup$ @infinitylord: Extrema is usually defined in such a way that differentiability is not assumed. For example, most books would say that $0$ is an extrema for the absolute value function. $\endgroup$ – Dave L. Renfro Nov 28 '16 at 15:55
  • $\begingroup$ Yes, that would make sense. $\endgroup$ – A curious one Nov 28 '16 at 15:58
1
$\begingroup$

A local extreme can be either a local minimum or a local maximum. Sometimes you just care that it is just one or the other, not which one.

$\endgroup$
  • $\begingroup$ Aha, that's what I thought, it was just weird that none of the books ever stressed this before. Or maybe they just assumed people would make the connection. $\endgroup$ – A curious one Nov 28 '16 at 15:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.