The correct option is A (0,2),(1,1) and (−1,1)
Calculate dydx (slope of a tangent)
dydx=d(x4−2x2+2)dx
dydx=4x3−4x
Solve the equation : dydx=0 (since slope of horizontal tangent is zero)
4x3−4x=0
4x(x2−1)=0
x=0,1,−1
The curve y=x4−2x2+2 have horizontal tangents at x=0,1 and −1. The corresponding points on the curve are (0,2),(1,1) and (−1,1).