How do you find the local extrema of #g(x)=-x^4+2x^2#?

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Answer 1 · 2018-02-03T09:58:41

#-1, 0, 1 # are the points of local extrema of this function.

#g(x) = -x^4 + 2x^2#

#rArr g'(x) = -4x^3 + 4x#

To find the points of Extrema put #g'(x) = 0#

#rArr -4x^3 + 4x = 0#

#rArr -4(x)(x-1)(x+1) = 0#

Thus the points of local extrema are:-
#x = 0 ;#

#x-1 = 0 rArr x = 1#

and #x+1 = 0 rArr x = -1#

And the Graph of the Function is given below :-

GeoGebra Classic app in Windows 10 was used to make this Graph