Nilai maksimum dari fungsi f(x) = 2x(x²-12)

Kita cari dulu f'(x)nya :
u = 2x v = x^2-12
u' = 2 v' = 2x

f'(x) = u'v + v'u
= 2 (x^2-12) + 2x (2x)
= 2x^2 - 24 +4x^2
=6x^2 - 24

Lalu masukkn rmsnya :
f'(x) = 0
6x^2 - 24 =0
6x^2 =24
x^2 = akar 4
x = 2

f(x) = 2x(x^2-12)
f(2) = 2(2) (2(2)^2-2)
= 4 (2(4)-2)
= 4 (6)
= 24
Jadi,nilai maksimumnya 24