Question

Tentukan nilai maksimum dan minimum pada interval f(x) = ( x-1 )³ pada interval [ -1,4 ]

Answer 1

F(x) = (x-1)³
f'(x) = 3×-3²
f'(-1) = 3(-1)-3
= -6 > nilai minimum
f'(4) = 3(4)-3
= 9 > nilai maksimum

Answer 2

f(x) = (x - 1)³
syarat stasioner, f'(x) = 0
3(x - 1)² = 0
x - 1 = 0
x = 1

nilai stasioner:
f(1) = (1 - 1)³ = 0

nilai stasioner pada ujung interval [-1 , 4]
f(-1) = (-1 - 1)³ = -8
f(4) = (4 - 1)³ = 27

nilai maksimum: 27
nilai minimum: -8

semoga membantu ya :)