Jawaban:

D. 144

Penjelasan dengan langkah-langkah:

f(x) = 2x³ + 3x² - 36x - 1

f'(x) = 6x² + 6x - 36

f'(x) = 0

6x² + 6x - 36 = 0

x² + x - 6 = 0

(x + 3)(x - 2) = 0

x = - 3 atau x = 2

interval - 4 ≤ x ≤ 5

f(-4) = 2(-4)³ + 3(-4)² - 36(-4) - 1

= 2(-64) + 3(16) + 144 - 1

= - 128 + 48 + 144 - 1

= 63

f(-3) = 2(-3)³ + 3(-3)² - 36(-3) - 1

= 2(-27) + 3(9) + 108 - 1

= - 54 + 27 + 108 - 1

= 80

f(2) = 2(2)³ + 3(2)² - 36(2) - 1

= 2(8) + 3(4) - 72 - 1

= 16 + 12 - 72 - 1

= - 45

f(5) = 2(5)³ + 3(5)² - 36(5) - 1

= 2(125) + 3(25) - 180 - 1

= 250 + 75 - 180 - 1

= 144 → maksimum