Jawabanmu

2014-05-07T13:30:19+07:00
f(x) = ax^2 + bx + c
f(1) = 2 --> 2 = a.2^2 +b.2 + c --> 4a + 2b + c = 2 .....(i)
f'(0) = 0 --> 2ax + b = 0 --> 2a.0 +b = 0 --> b = 0.....(ii)
f'(1) = 2 --> 2ax +b = 2 --> 2a.1 + b = 2 --> 2a + b = 2 ....(iii)
Dari persamaan (ii), b = 0
Masukkan ke persamaan (iii), 2a + b = 2 --> 2a + 0 = 2 --> 2a = 2 --> a = 1
Dari hasil tersebut, masukkan ke persamaan (i) :
4a + 2b + c = 2 --> 4.1 + 2.0 + c = 2 --> 4+c = 2 --> c=-2
f(x+1) = a(x+1)^2 + b(x+1) + c
f(x+1) = 1(x+1)^2 + 0(x+1) - 2
f(x+1) =  x^2 + 2x + 1 - 2
f(x+1) = x^2 + 2x - 1