Find f if f"(theta)=sin (theta) + cos (theta), f(0)=3, and f'(0)=4

Replace the x with theta :

f''x = sin x + cos x

f'x  = - cos x  + sin x + c

f'0 = -1 + 0 + c =4

c = 5

f'x = -cos x + sin x + 5
fx = -cos x  - sin x  + c
f0  = -1  + c = 3

c = 4

fx = -cos x - sin x + 4

Hope this helps