Find the absolute maximum and minimum values of f(x,y)=y2+x2−6x−1 on the set D where D is the closed triangular region with vertices (12,0), (0,7), and (0,−7).


a. The critical points of f are:

b. Find a linear equation for the side of the boundary of the region D between (12,0) and (0,7).

y=

Along this side, f can be expressed as a function of one variable

g(x)=f(x,_______) = _______________


c. List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D.

d. Find the function’s absolute maximums and minimums and where they occur.