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

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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...
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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). read less
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