nilai stasioner fungsi f(x)

[tex]\displaystyle f(x)=x^3-3x^2-24x-7\\\\f'(x)=3x^2-6x-24\\f'(x)=3(x^2-2x-8)\\f'(x)=3(x-4)(x+2)\\0=3(x-4)(x+2)\\x=-2\vee x=4\\\\f(4)=4^3-3(4)^2-24(4)-7\\f(4)=64-48-96-7\\f(4)=16-96-7\\f(4)=-80-7\\\boxed{\boxed{f(4)=-87}}\\\\f(-2)=(-2)^3-3(-2)^2-24(-2)-7\\f(-2)=-8-12+48-7\\f(-2)=-12+40-7\\f(-2)=-12+33\\\boxed{\boxed{f(-2)=21}}[/tex]

Diketahui :
f (x) = x³ - 3x² - 24x - 7

Ditanya : nilai stasioner fungi f (x) ?

Dijawab :
Nilai stasioner dicapai saat f'(x) = 0
f (x) = x³ - 3x² - 24x - 7

f'(x) = 3x³⁻¹ - 6x²⁻¹ - 24
f'(x) = 3x² - 6x - 24
f'(x) = x² - 2x - 8

Syarat f'(x) = 0
f'(x) = 0
x² - 2x - 8 = 0
(x - 4) (x + 2) = 0
x = 4, x = -2

Untuk x = 4
f (4) = 4³ - 3 (4)² - 24 (4) - 7
f (4) = 64 - 3 (16) - 96 - 7
f (4) = 64 - 48 - 96 - 7
f (4) = -87

Untuk x = -2
f (-2) = (-2)³ - 3 (-2)² - 24 (-2) - 7
f (-2) = -8 - 3 (4) + 48 - 7
f (-2) = -8 - 12 + 48 - 7
f (-2) = 21

Jadi, nilai stasioner dari fungsi f (x) adalah -87 dan 21