# Argmax - all maximizer positions

Generally the Argmax function returns one position, where a function is maximized. Is there a easy way to obtain a list of rules for all maximizer points?

f[x_] = LaguerreL[6, x];

ArgMax[{f[x], 0 < x < 10}, x] // N

(* 8.39907 *)


The maxima occur where the derivative is zero and the second derivative is negative.

(argMax = Solve[{f'[x] == 0, f''[x] < 0}, x, Reals]) // N

(* {{x -> 2.11297}, {x -> 8.39907}} *)

Plot[f[x], {x, 0, 10},
Epilog -> {Red, AbsolutePointSize[4],
Point[{x, f[x]} /. argMax]}]


• Thank you very much! – oyy Nov 25 '20 at 16:21