Question

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

Answer 1

Answer:

x = -1 ,+1

Step-by-step 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.

$\frac{dy}{dx}=-4x^{3}+4x$

Now equate it's derivative to zero.

$\frac{dy}{dx}=-4x^{3}+4x$=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.