Tentukan interval fungsi naik' interval fungsi turun, dan nilai stasioner dari fungsi f(x) = x(x-1)^2

f(x) = x(x-1)² = x(x²-2x+1) = x³-2x²+x
fungsi naik, turunan > 0
3x² - 4x + 1 > 0
(3x - 1)(x - 1) > 0
x < 1/3 atau x > 1
fungsi turun, turunan < 0
3x² - 4x + 1 < 0
(3x - 1)(x - 1) < 0
1/3 < x < 1
nilai stasioner, turunan = 0
3x² - 4x + 1 = 0
(3x - 1)(x - 1) = 0
x = 1/3 dan x = 1
f(1/3) = (1/3)³ - 2(1/3)² + 1/3
= 1/27 - 2/9 + 1/3
= 1/27 - 6/27 + 9/3
= 4/27
f(1) = 1³ - 2(1) + 1 = 0
titik stasioner (1/3,4/27) (1,0)