Consider the function f(x) whose second derivative is f′′(x)=8x+5sin(x). If f(0)=2 and f′(0)=3, what is f(x)
f" = 8x + 5sinx
f' = 4x^2 - 5cosx + C
f'(0) = 0 - 5 + C = 3
so,
f'(x) = 4x^2 - 5cosx + 8
Now repeat the logic to find f(x)
f' = 4x^2 - 5cosx + C
f'(0) = 0 - 5 + C = 3
so,
f'(x) = 4x^2 - 5cosx + 8
Now repeat the logic to find f(x)