Question

what are the coordinates of the points at which the slope of the function with the equation y = x^4 - 8x^2 is equal to zero ?

Answer 1

y' = 4x^3 -16x = 4x(x^2-1)
0 at x = 0
0 at x = 1
0 at x =-1
so at
( 0, 0 )
( 1, -7
(-1, -7)

Answer 2

y' = 4 x^3 - 16 x = 4x (x^2 - 4)
zero at x = 0, 2 , -2
so
(0, 0)
(-2,-16)
(+2,-16)