The points on the curve y=x4−4x3+4x2+1 at which the tangents are parallel to x-axis are

y=x4−4x3+4x2+1 Slope=(dydx)(x1,y1)=4x13−12x12+8x1     The points which tangent are  parallel to x-axis are  (dydx)(x1,y1)=0 ⇒4x13−12x12+8x1=0 ⇒4x1(x12−3x1+2)=0 ∴   x1=0,  1,2      y1=1,  2,1}⇒(0,1),(1,2),(2,1)