Question

Diketahui f(x) = ax^2 + bx +c dengan f(1)= 2, f'(0)=0, dan f'(1)=2 fungsi tersebut adalah
a. x^2 +1
b. x^2 -1
c. x^2 - 2x - 3
d. 1/2(x^2 + x - 1/2)
e. x^2 + x -2

Answer 1

F (x) = ax² + bx + c
f ' (x) = 2ax + b

f ' (0) = 2a(0) + b
(=) 0 + b
= b

b = 0

f ' (1) = 2a(1) + 0
(=) 2a

2a = 2
a = 2 / 2
a = 1

f (x) = ax² + bx + c
f (x) = x² + c
f (1) = (1)² + c
1 + c = 2
c = 2 - 1
c = 1

f (x) = ax² + bx + c
f (x) = x² + 1