I have prepared a geometric intuition of Multivariable Mean Value Theorem for function of two variables in my own understanding after reading several books. But I am not sure whether is it correct or not. also, i am not able to find any geometrical interpretation on multidimensions so far.
I am providing a link to this topic. Please, if anyone finds the time to go through this, please help.
I am Providing this PDF because there are hand drawn figures which are not available on the internet directly and it does not require any formula, I have only explained what that figure is.
https://drive.google.com/file/d/1fpM249z_XK1ytzdElzNYNQamG_jY4r-O/view?usp=sharing