How can I derive the below form for a function of two variables. The function is twice differentiable.
$f(y,x_1)$ and $f(y,x_2)$, then $\forall x_1,x_2$ $\exists c$ such that $x_1 < c <x_2$
$f(y,x_1) - f(y,x_2) = (x_1 - x_2)f'(y,x_1) - \frac{f''(y,c)}{2} (x_2 - x_1)^2$
The paper says, it is based on Taylor expansion. But using Taylor series, I am not able to get rid of the c coefficient of f'.