Lagrange multipliers

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To optimize a function $f (x, y)$ subject to a constraint $g (x, y) = c$ , the gradients must be parallel at an extremum: $
abla f=\lambda\nabla g $. S o l v e t hi s v ec t or e q u a t i o n t o g e t h er w i t h t h eco n s t r ain t e q u a t i o n f or$ x $,$ y $, an d$ \lambda $. E a c h so l u t i o n p o in t i s a c an d i d a t e; e v a l u a t e$ f$ at all candidates to identify the maximum and minimum values.

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#	Title	Difficulty
135110	(Sensitivity) Certainly … has	Medium
135111	(Theory behind …) When … is solved for …, it gives a…	Medium
135112	(d) Draw the pointed curve … to see why it is not…	Medium
135113	(No maximum) Find a point on the line … where … is…	Medium
135114	Find the minimum of … if … is restricted to the planes…	Medium
135115	(a) Find by Lagrange multipliers the volume … of the largest box…	Medium
135116	the plane … and a vector perpendicular to the plane	Medium
135117	Minimize … on the plane … one constraint and one multiplier	Medium
135118	At the absolute minimum of …, the derivatives ______ are zero	Medium
135119	Find the minimum of … with the constraints … and … and…	Medium
135121	With an inequality constraint …, the multiplier at the minimum satisfies	Medium