Question

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

Answer 1

\[f \prime \prime (\theta)=\sin \theta +\cos \theta\]
\[f \prime (\theta) =-\cos \theta + \sin \theta +c\]
\[f \prime (0) =-1+0+c=4\]
\[c=5\]
\[f \prime (\theta) =-\cos \theta + \sin \theta +5\]
\[f (\theta) =-\cos \theta - \sin \theta +c\]
\[f(0)=-1+c=3\]
\[c=4\]
f(θ)=−cosθ−sinθ+4