Question

OK, so I thought I had this one but I'm not getting the right answer

Consider the function f(x) whose second derivative is f''(x) = 2 x + 8 \sin (x). If f(0) = 2 and f'(0) = 2, what is f(x)?

Answer 1

\(f ''(x)=2x+8\sin x\\
f'(x)=\int f''(x)\;dx\\
f(x)=\int f'(x)\;dx\)

Answer 2

I actually just had to do a little bit more, I was almost there and got it
I ended up with 1/3x^3-8sin(x)+10x+2, just had to get the 10x+2 part figured out

Answer 3

When you integrate, you'll be left with a constant of integration, which you solve for using the given points.