For the curve y = 4x3 - 2x5 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)