For the curve y =

The given curve y = 4x³ – 2x⁵

Then, the slope of the tangent at the point (x, y) is 12x² – 10x⁴

The equation of the tangent at (x,y) is given by,

Y – y = (12x² – 10x⁴)(X – x) ………….(1)

When the tangent passes through the origin (0,0), then X =Y=0

Then equation (1) becomes,

-y = (12x² – 10x⁴)(– x)

⇒ y = (12x³ – 10x⁵)

Also, we have y = 4x³ – 2x⁵

⇒ (12x³ – 10x⁵) = 4x³ – 2x⁵

⇒ 8x⁵ – 8x³ = 0

⇒ x⁵ – 2x³ = 0

⇒ x³(x² – 1) = 0

⇒ x = 0 , 1

When x = 0 then y = 0

When x = 1 then y = 2

And when x = -1 then y = -2

Therefore, the required points are (0, 0), (1,2) and (-1, -2).