Dik:
panjang = 2x+6 cm
lebar = 5-x cm
Dit: luas maks.
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Luas = panjang × lebar
Luas = (2x+6)(5-x)
Luas = 10x-2x²+30-6x
Luas = -2x²+4x+30
f(x) = -2x²+4x+30
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Supaya luas maks.
turunan f(x) harus = 0
0 = (-2x²+4x+30)'
0 = -4x + 4
4x = 4
x = 4÷4
x = 1,
f(x) = -2x²+4x+30
maka f(1) = -2(1)²+4(1)+30
f(1) = -2+4+30
= 32 cm² ✔️
Jawaban:
L = p x l
= (2x + 6) x (5 - x)
= 10x - 2x² + 30 - 6x
= -2x² - 4x + 30
____________ :-2
= x² + 2x - 15
= (x + 5) (x - 3)
x1 = -5 dan x2 = 3
misal: x = -5 >> L = (2x + 6) (5 - x)
= (2(-5) + 6)) (5 - (-5))
= -4 x 10
= -40 cm²
misal: x = 3 >> L = (2x + 6) (5 - x)
= (2(3) + 6) (5 - 3)
= 12 x 2
= 24 cm²
Maka luas maksimum nya adalah 24 cm².
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