Question -
Answer -
The equation of the given curve is y =4x3 − 2x5.
Therefore, the slope of the tangent at apoint (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).