Nilai maksimum dari f(x)=-2x^2-2x+13 adalah...

Materi: Turunan Fungsi

f(x) = -2x^2 -2x + 13
f'(x) = -4x - 2
Agar maksimum haruslah f'(x) = 0
0 = -4x - 2
2 = -4x
x = -1/2.
Substitusikan x ini ke f(x)
f(-1/2) = -2(-1/2)^2 - 2(-1/2) + 13
= -2(1/4) + 14
= 13 1/2

Bab Persamaan Kuadrat
Matematika SMP Kelas VIII

f(x) = -2x² - 2x + 13
a = -2; b = -2; c = 13

sumbu simetri = -b/2a
sumbu simetri = -(-2)/(2 . -2)
sumbu simetri = -1/2

f(-1/2) = -2 . (-1/2)² - 2 . (-1/2) + 13
f(-1/2) = -2 . (1/4) + 1 + 13
f(-1/2) = -1/2 + 1 + 13
f(-1/2) = 13 1/2

nilai maksimum = 13 1/2