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Let S be the set of all values of x for which the tangent to the curve y = f(x) = x³ − x² − 2x at (x, y) is parallel to the line segment joining the points (1, f(1)) and (−1, f(−1)), then S is equal to:

1. {1/3, 1}
2. {−1/3, −1}
3. {1/3, −1}
4. {−1/3, 1}

Correct answer: {−1/3, 1}

Solution

The correct option is right because the slope of the tangent line at a point on the curve is determined by the derivative of the function, which must equal the slope of the line segment between the given points. By calculating the derivative and finding where it matches the slope of the line segment, we identify the values of x that satisfy the condition.

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