Find f '(x) and f(x).

Question

f ''(x) = 36x,    f''(0) = 3,    f(0) = 2

Answer 1

I think that you mean: f"(x) = 36x, f'(0) =3, and f(0) = 2

Since f"(x) = 36x, f'(x) = ∫36xdx = 18x² + C₁

f'(0) = 3, so 0 + C₁ = 3, C₁ = 3

f'(x) = 18x² + 3

f(x) = ∫f'(x)dx = ∫(18x² + 3)dx

f(x) = 6x³ + 3x + C₂

f(0) = 2, so 0 + 0 + C₂ = 2, C₂ = 0

f(x) = 6x³ + 3x + 2