Answer:
x = -1 ,+1
Step-by-step explanation:
Let y be a function of x given in question
[tex]y =-x^{4}+2x^{2}[/tex]
Simply differentiate it to get it's derivative and then equate to zero to find it's extremams.
[tex]\frac{dy}{dx}=-4x^{3}+4x[/tex]
Now equate it's derivative to zero.
[tex]\frac{dy}{dx}=-4x^{3}+4x[/tex]=0
[tex]x=x^{3}[/tex]
So, after solving we get
x=0,1,-1
Now by graphical interpretation we can observe that it is even function thus it is symmetric about Y axis. Also it passes through origin.
At minus and plus infinity of x y tends to minus infinity.
Also check nearby values to 1 or -1.
Thus at -1 and +1 there is maxima symmetrically.
