The maximum value of the function f(x) = 2x³ − 15x² + 36x + 1 on the interval [1, 5] is:

The maximum value of the function f(x) = 2x³ − 15x² + 36x + 1 on the interval [1, 5] is:

• A. 56
• B. 24
• C. 1
• D. 48

Answer: A) 56

Explanation: f'(x) = 6x² − 30x + 36 = 6(x² − 5x + 6) = 6(x − 2)(x − 3). Critical points: 2, 3. f(1) = 2 − 15 + 36 + 1 = 24. f(2) = 16 − 60 + 72 + 1 = 29. f(3) = 54 − 135 + 108 + 1 = 28. f(5) = 250 − 375 + 180 + 1 = 56. Maximum is 56.