Question

Find the points on the curve y = x³ – 2x² – x at which the tangent lines are parallel to the line y = 3x – 2.

Answer 1

Let P(x₁, y₁) be the required point. The given curve is

Since the tangent at (x₁, y₁) is parallel to the line y = 3x - 2

Slope of the tangent at (x₁, y₁) = slope of the line, y = 3x - 2

Since (x₁, y₁) lies on the curve(i). Therefore