For the curve y = 4x^{3} - 2x^{5} find all the points at which tangents passes through origin

Let (x1, y1) be point on the curve where tangent is such that it passes through origin. To find slope we need

So equation of tangent becomes

This passes through origin

So

On simplification this gives

But since (x1, y1)lies on curve so

Therefore

So

Which gives

When

So required points are (0, 0), (1, 2) (-1, -2)