jika 9pangkatx-1=3 pangkat 1-4x maka f(y)=y² +2xy + 4x² mempunyai nilai minimun sama dengan

jawab

9^(x-1) = 3^(1- 4x)
(3^2)^(x-1) = (3)^(1-4x)
2(x - 1) = 1 - 4x
2x - 2 = 1 - 4x
6x = 3
x= 1/2

f(y) = y² + 2xy + 4x² dan x = 1/2
f(y)= y² + 2(1/2)(y)+ 4(1/2)²
f(y) = y² + y + 1

f'(y) =0
2y + 1= 0
y = - 1/2
f (1/2) = (1/2)² + (1/2) + 1
f(1/2) = 7/4
nilai minimum = 7/4