Question

find f(x) given that the slope of the tangent line to the graph of f at any point is f'(x):

f'(x)=eˣ + x and the graph of f passes through (0,3)

Answer 1

\[f(x)=e^x+\frac{x^2}{2}+C\]
\[f(0)=e^0+\frac{0^2}{2}+C=3\]
\[1+C=3\]\[C=2\]
\[f(x)=e^x+\frac{x^2}{2}+2\]