Find f by solving the initial value problem

Question

f '(x) = 6x² + 6x − 2; f(2) = 7

Answer 1

f'(x) = 6x^2+6x-2

f(x) = 2x^3 + 3x^2 -2x + c where c= a constant

f(2) = 7 = 16+12-4 + c

c = 7-24 = - 17

f(x) 2x^3 +3x^2 -2x -17