Question

For the curve $y = 4x^3 − 2x^5$ , find all the points at which the tangents passes through the origin.

Answer 1

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

$\frac {dy}{dx}$ = 12x2 - 10x4

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 x = 0, y = 4(0)3 - 2(0)5 = 0.

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).