Question

For the curve y = 4x³ − 2x⁵, find all the points at which the tangents passes through the origin.

Answer 1

The equation of the given curve is y = 4x³ − 2x⁵.

Therefore, the slope of the tangent at a point (x, y) is 12x² − 10x⁴.

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

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

Therefore, equation (1) reduces to:

Also, we have

When x = 0, y =

When x = 1, y = 4 (1)³ − 2 (1)⁵ = 2.

When x = −1, y = 4 (−1)³ − 2 (−1)⁵ = −2.

Hence, the required points are (0, 0), (1, 2), and (−1, −2).