We have to find f(x).
First we have to integrate f'(x) and then satisfy the initial condition f(0).
Integrating f'(x):
[tex]f(x)=\int (x^2+3)dx=\frac{x^3}{3}+3x+C[/tex]
We can then replace x with x=0 and f(x) with f(0)=21 to find the value of the constant C:
[tex]\begin{gathered} f(0)=21=\frac{0^3}{3}+3\cdot0+C \\ C=21 \end{gathered}[/tex]
Then, the function f(x) is:
[tex]f(x)=\frac{x^3}{3}+3x+21[/tex]
Answer: f(x) = x^3/3 + 3x + 21 (Option A)
