tentukan nilai maksimum dari fungsi f(x)=3x³-3x
Matematika
wahyu1519
Pertanyaan
tentukan nilai maksimum dari fungsi f(x)=3x³-3x
1 Jawaban
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1. Jawaban Anonyme
turunan f = 3.3x² - 3
= 9x² - 3
maksimum jika turunannya sama 0
9x² - 3 = 0
9x² = 3
x² = 1/3
x = √1/3 atau x = -√1/3
subs ke f(x)
f(√1/3) = 3(√1/3)³-3(√1/3)
=3.(1/3)(√1/3) - 3(√1/3)
=(√1/3) - 3(√1/3)
= -2(√1/3)
f(-√1/3) = 3(-√1/3)³-3(-√1/3)
=3(-1/3)(√1/3) + 3(√1/3)
= -(√1/3) + 3(√1/3)
= 2(√1/3)