Question

Jika f(x) = (1 + 4x)^2 (2 - x) maka 6. f'( 1 ) + f'( -1 ) = ........

Answer 1

Dengan f(x) = u.v

u = (1+4x)²
v = (2-x)

Berlaku:

u' = 2.(1+4x)¹.(4)
u' = 8(1+4x)

v' = -1

Sehingga:
f'(x) = u'.v + u.v'
f'(x) = 8(1+4x)(2-x) + (1+4x)²(-1)
f'(x) = 8(1+4x)(2-x) - (1+4x)²

Dengan nilai:
f'(1) = 8(1+4)(2-1) - (1+4)²
f'(1) = 15

f(-1) = 8(1-4)(2+1) - (1-4)²
f(-1) = -81

Maka:
6.f'(1) + f(-1)
= 6(15) + (-81)
= 90 - 81
= 9