let us consider I have a function $f(x,y)$, I know a value $f_0=f(x=0,y=0)$ but I don't know how $f$ is done. By the way I know his partial derivatives $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$. I want to plot $f$ in a 3D plot respect to $x$ and $y$ in an interval $x_L\leq x\leq x_U$ and $y_L\leq y\leq y_U$.
Which is the relation that I should use to do that? How to evaluate $f$?
I tought about:
$$f(x,y)=f_0+something$$
which depends on derivatives. Am i right?
EDIT:
After some calculation: $$\frac{\partial f}{\partial x}=a$$ with $a$ scalar. $$\frac{\partial f}{\partial y}=b$$ with $b$ scalar.
And $f_0=c$ with $c$ scalar