Penjelasan dengan langkah-langkah:

f(x) = 1/3x³ - x² - 3x + 2

f'(x) = x² - 2x - 3

titik stasioner pada saat f'(x) = 0.

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 V x = -1

nilai stasioner :

f(3) = 1/3(3)³ - (3)² - 3(3) + 2

f(3) = 9 - 9 - 9 + 2

f(3) = -7

f(-1) = 1/3(-1)³ - (-1)² - 3(-1) + 2

f(-1) = -1/3 + 1 + 3 + 2

f(-1) = 11/3

x min saat x = -2, dan x max saat x = 1 :

f(-2) = 1/3(-2)³ - (-2)² - 3(-2) + 2

f(-2) = -8/3 - 4 + 6 + 2

f(-2) = 4/3

f(1) = 1/3(1)³ - (1)² - 3(1) + 2

f(1) = 1/3 - 1 - 3 + 2

f(1) = -5/3

Nilai max : 11/3 = a

Nilai min : -7 = b

a + b = 11/3 - 7 = -10/3

Mapel : Matematika

Kelas : 11

Materi : Turunan