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Question
For the curve y = 4x3 − 2x5, find all the points at which the tangents passes through the origin.
Solution
The equation of the given curve is y = 4x3 − 2x5.
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).
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