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Are they the same? (a) Find the maximum value of $f(x)$; (b) find the maximum of $f(x)$.

I was told by someone that "value" is unnecessary. Moreover, Are (c) and (d) the same?

(c) Find the local maxima of $f(x)$; (d) find the local maximum values of $f(x)$.

Haoran Chen
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  • This could depend on the context. If you have both those listed as separate things in a problem, then (b) most likely wants you to find the $x$ such that $f(x)$ is the maximum value, while (a) just wants you to find the maximum value $f(x)$ – Lorago Sep 07 '22 at 13:17
  • I believe in terms of grammar, "maxima" is used a a noun while "maximum" as an adjective. When you say find the local maxima, it is quite clear what is needed to be found (all local maximas of $f$), while on the other hand if you say find the local maximum values of $f$, it is expected that you say in what interval (or any subset) – PCeltide Sep 07 '22 at 13:18
  • "Maxima" is the plural of the noun "maximum". – Andreas Blass Sep 07 '22 at 15:43

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