Solve the following initial value problem. f″(x)=24x^2+6x−6, f(0)=13, f(1)=21

Answer 1

f"(x) = 24x^2 +6x -6

f'(x) = 8x^3 +3x^2 -6x + C

f(x) = 2x^4 + x^3 -3x^2 + Cx + K

f(0) = 13, K=13

f(1) = 21 = 2+1-3+C+ 13

C = 21-13 = 8

f(x) = 2x^4 + x^3 -3x^2 + 8x + 13

f'(x) = 8x^3 +3x^2 -6x +6

f"(x) = 24x^2 +6x -6