could any one just tell me in a short what is the geometric idea of this theorem?
"let $u:\Omega\subseteq\mathbb{R}^2\rightarrow \mathbb {R}$,$p=(x_0,y_0)\in\Omega$, $u_x,u_y$ exist at every point in a neighborhood of $p$ and continous at $p$ Then for sufficiently small $s,t$ in $\mathbb{R}$,
$$u(x_0+s,y_0+t)-u(x_0,y_0)=su_x(x_0+s^*,y_0+t^*)+tu_y(x_0,y_0+t^*)$$ with $|s^*|<|s|,|t^*|<|t|$