Nilai stasioner fungsi f(x) = x kuadrat 3 - 3xpangkat2 - 24x -7 adalah....

f(x) = x³ - 3x² - 24x - 7
f'(x) = 3(1)x² - 2(3)x - 1(24)
f'(x) = 3x² - 6x - 24

f(x) stasioner ⇒ f'(x) = 0
3x² - 6x - 24 = 0
------------------------- ÷ 3
x² - 2x - 8 = 0
(x - 4) (x + 2) = 0
x1 = 4
x2 = -2

⇒Nilai stasioner pada x = 4
f(4) = (4)³ - 3(4)² - 24(4) - 7
f(4) = 64 - 48 - 96 - 7 = -87

⇒Nilai stasioner pada x = -2
f(-2) = (-2)³ - 4(-2)² - 24(-2) - 7
f(-2) = -8 - 16 + 48 - 7 = 17

Matematika XI SMA
Fungsi Stasioner

Pembahasan :
f(x) = x³ - 3x² - 24x - 7
f'(x) = 3x² - 6x - 24
0 = 3x² - 6x - 24
x² - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 V x = -2

Untuk x = 4, Nilai stasionernya...
f(x) = x³ - 3x² - 24x - 7
f(x) = 4³ - 3(4)² - 24(4) - 7
f(x) = 64 - 48 - 96 - 7
f(x) = -87

Untuk x = -2, nilai stasionernya..
f(x) = x³ - 3x² - 24x - 7
f(x) = (-2)³ - 3(-2)² - 24(-2) - 7
f(x) = -8 - 3(4) + 48 - 7
f(x) = -8 - 12 + 48 - 7
f(x) = 17