Question

At what value(s) of x does f(x) = -x4 + 2x2 have a relative maximum? (4 points)

Answer 1

x = -1 ,+1

Explanation:

Let y be a function of x given in question

`y =-x^(4)+2x^(2)`

Simply differentiate it to get it's derivative and then equate to zero to find it's extremams.

`(dy)/(dx)=-4x^(3)+4x`

Now equate it's derivative to zero.

`(dy)/(dx)=-4x^(3)+4x`=0

`x=x^(3)`

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.