Find f. f '''(x) = cos(x), f(0) = 9, f '(0) = 1, f ''(0) = 7

Answer 1

f''(x) = ∫cosxdx = sinx + C₁; f''(0) = sin0 + C₁ = 7; C₁ = 7; f''(x) = sinx + 7.

f'(x) = ∫(sinx + 7)dx = - cosx + 7x + C₂; f'(0) = - cos0 + 7·0 + C₂ = 1; C₂ = 2; f'(x) = - cosx + 7x + 2.

f(x) = ∫(- cosx + 7x + 2)dx = - sinx + 7x²/2 + 2x + C₃, f(0) = - sin0 +0 + 0 + C₃ = 9; C₃ = 9.

f(x) = -sinx + 7x²/2 + 2x + 9