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' = 4x^2 - 5cosx + C
f'(0) = 0 - 5 + c = 2
C = -7 and so
f'(x) = 4x^2 - 5cosx - 7
Now do all that again to find f(x)
f'(0) = 0 - 5 + c = 2
C = -7 and so
f'(x) = 4x^2 - 5cosx - 7
Now do all that again to find f(x)