Consider the function f(x) whose second derivative is f''(x)=5x+2sin(x). If f(0)=3 and f'(0)=3, what is f(3)?

Answer 1

f" = 5x+2sinx
f' = 5/2 x^2 - 2cosx + c
f'(0)=3, so
0-2+c=3
c=5
so, f' = 5/2 x^2 - 2cosx + 5

f = 5/6 x^3 - 2sinx + 5x + c
f(0)=3, so
0-0+0+c=3
c=3
so, f=5/6 x^3 - 2sinx + 5x + 3

I assume you can now find f(3)