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

Question

2539 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-03T09:58:41

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

$g (x) = - x^{4} + 2 x^{2}$ $g(x) = -x^4 + 2x^2$

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

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

How do you find the local extrema of g(x)=-x^4+2x^2g(x)=−x4+2x2g(x)=-x^4+2x^2?