The point on the curve y = x³ − 11x + 5 at which the tangent is y = x − 11 is:

The point on the curve y = x³ − 11x + 5 at which the tangent is y = x − 11 is:

• A. (2, −9)
• B. (3, −1)
• C. (4, 13)
• D. (1, −5)

Answer: A) (2, −9)

Explanation: Slope of given tangent is 1. dy/dx = 3x² − 11 = 1 → 3x² = 12 → x² = 4 → x = 2 or −2. For x = 2, y = 8 − 22 + 5 = −9. Tangent at (2, −9): y + 9 = 1(x − 2) → y = x − 11. Matches. For x = −2, y = −8 + 22 + 5 = 19, tangent y − 19 = 1(x + 2) → y = x + 21 ≠ given line.