The function f(x) = 2x³ − 3x² − 36x + 7 has a local maximum at x equal to:

The function f(x) = 2x³ − 3x² − 36x + 7 has a local maximum at x equal to:

• A. −2
• B. 3
• C. 2
• D. −3

Answer: A) −2

Explanation: f'(x) = 6x² − 6x − 36 = 6(x² − x − 6) = 6(x − 3)(x + 2). f''(x) = 12x − 6. At x = −2, f''(−2) = −24 − 6 = −30 < 0 → local max. At x = 3, f''(3) = 36 − 6 = 30 > 0 → local min.