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

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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

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