maximum minimum Solution This function is subject to the f

maximum =  
minimum =  

Solution

.

This function is subject to the following constraint:

Using Lagrange multipliers,

Solving equation (2), (3) and (4) gives us the set of equations:

Solving these equations gives usandrespectively.

Plugging these values into equation (5) gives us:

Solving this equation gives us

If, then

If, then

At:

At:

Thus,have a maximum atand a minimum at.

Therefore, the maximum value is 6 and the minimum value is -6