Find the particular solution that satisfies the differential equation and the initial condition

Question

Find the particular solution that satisfies the differential equation and the initial condition.

f’(x)=12x^2; f(0)=-8

Answer 1

f'(x) = 12x²

f(x) = ∫f'(x)dx = ∫(12x²)dx = 4x³ + C

Since f(0) = 8, 4(0)³ + C = -8. So, C = -8.

f(x) = 4x³ - 8