For the curve `y=4x^3-2x^5` find all points at which the tangent passes through the origin.

Answer

The points are `(0,0),(1,2)`, and `(-1,-2)`.

Explanation

Given the equation of curve is `y=4 x^{3}-2 x^{5}`.
$$ \therefore \frac{d y}{d x}=12 x^{2}-10 x^{4} $$
Now, slope of the tangent at a point `(x, y)` is
`12 x^{2} - 10 x^{4}`.


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