diketahui f'(x)=ax^2+bx. Jika f'(1)=2 dan f'(-1)=10 maka rumus f(x) adalah

f'(x) = ax^2 + bx
f'(1) = a(1)^2 + b(1) = 2 ===> a + b = 2
f'(-1) = a(-1)^2 + b(-1) = 10 => a - b = 10
---------------------------------------------------- +
................................................. 2a = 12 => a = 6
a + b = 2 => 6 + b = 2 => b = -4
f'(x) = ax^2 + bx = 6x^2 - 4x

f(x) = ∫ (6x^2 - 4x) dx
= 6/3 x^3 - 4/2 x^2 + C
= 2x^3 - 2x^2 + C