tentukan selisih nilai maksimal dan minimum dari fungsu f(x) satu pertiga X pangkat 3 + setengah X kuadrat - 2X + 5

f(x) = ⅓x³ + ½x² - 2x + 5
f'(x) = x² + x - 2

Nilai min dan max ddpt saat f'(x) = 0

x² + x -2 = 0
(x + 2)(x - 1) = 0
x = -2 v x = 1

Masukkan

f(-2)
= 1/3 (-2)³ + 1/2 (-2)² - 2(-2) + 5
= 1/3 (-8) + 1/2 (4) + 4 + 5
= -8/3 + 2 + 4 + 5
= 11 - 8/3
= 25/3

f(1)
= 1/3 (1)³ + 1/2 (1)² - 2(1) + 5
= 1/3 + 1/2 - 2 + 5
= 1/3 + 1/2 + 3
= 2/6 + 3/6 + 18/6
= 23/6

25/3 - 23/6
= 50/6 - 23/6
= 27/6