I've just started multi dimensional calculus, among which Langrange's Multipliers. I have some questions which will help me grasp the concepts since I'm a very curious guy... a) What are you finding exactly with this technique? b) What is the constraint? c) What does the extra variable represent? d) Is there another more intuitive but less effiecient way to obtain the same result? My lecturer is a very poor teacher and just wants to get on with the syllabus I guess... I would like an explanation on the actual graph of the function and not about the practical usage of it such as in economics... P.S. I understood the reasoning behind partial differentiation but I'm still shakey on the fact that in 3D planes you can only find a general gradient for each axis and not a single general one. Thanks!