Question

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

0 and -1 only
0 and 1 only
-1, and 1 only
0 only

Answer 1

take the derivitive
f'(x)=-4x^3+4x
find where it equals 0
0=-4x(x^2-1)
0=-4x(x-1)(x+1)
at x=-1, 0, 1

those are critical points
put those on number line
test points between to see if positive or negative
f'(-2)=(+)
f'(-0.5)=(-)
f'(0.5)=(+)
f'(2)=(-)
see attachment
remember the max is where the slope changes from positive to negative
at -1 and 1 only