Question

Suppose that f has a continuous second derivative for all x, and that f(0)=1, f'(0)=2, and f''(0)=0. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point (0,5) is on the graph of g.
- Find g''(0).

Answer 1

g"(x) = (6x+2)f' + (3x^2+2)f" + (3x^2+2)f'^2 + (x^3+2x+5)f"
g"(0) = 2*2 + 2*0 + 2*2^2 + 5*0 = 12