Find the points on the curve `y=x^3-2x^2-x` at which the tangent lines are parallel to the line `y=3x-2` .

Answer

Points are `(2,-2)` and `(frac{-2}{3}, frac{-14}{27})`.

Explanation

Given the equation of curve is `y=x^{3}-2 x^{2}-x`

`\frac{d y}{d x}=3 x^{2}-4 x-1`

`\therefore` At `(x_1 , y_1) ` slope of tangent `m_{1} = 3x_{1}^{2} – 4x_{1}-1`

Slope of line `y=3 x-2`

`m_{2}=3`

Since, the tangent is parallel to line
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