Calculus question

Question

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

f "(x) = 4,    f '(2) = 12,   f(2) = 19

Answer 1

f''(x = 4

f'(x) = 4x + C

12 = 4(2) + C

4 = C

f'(x) = 4x + 4

f(x) = 2x² + 4x + C

19 = 2(2)² + 4(2) + C

3 = C

f(x) = 2x² + 4x + 3