Find a point on the curve `y=x^3-3x` where the tangent is parallel to the chord joining `(1,\ -2)` and `(2,\ 2)` .

Answer

`y=+frac{2 sqrt{7}}{3 sqrt{3}}` and ` y=-frac{2 sqrt{7}}{3 sqrt{3}}`

Explanation

Given,
$$ y=x^{3}-3 x $$
As tangent is parallel to the chord passing through given points, Therefore there slopes will be equal.


Slope of chord,
$$
\mathrm{m}=\frac{2+2}{2-1}=4
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