Differentiation Functions

A function

has a saddle point at

if

and has both positive and negative values around



where

means

order continuous

If

changes from positive to negative at

, then

is a local max

If

changes from negative to positive at

, then

is a local min

If

and

,

then there exists a number

,

such that

Maximize:

subject to

Let:

Solve the system of equations:

Enter solved values of

into

and identify min and max.

Make sure solutions make sense.