Question

locate any relative maxima, minima or saddle points of the function:z= x^2 -2x +y^2 -6y+11

Answer 1

First look for the critical points of f by setting \(f_x=0, f_y=0\). Then substitute the crit. points in the ff quantity:
\[D=f_{xx}f_{yy}-(f_{xy})^2\]
If D<0, then the critical point is a saddle point.
If D>0 and \(f_{xx}\geq0,\), then the critical point is a minimum.
If D>0 and \(f_{xx}<0\), then the critical point is a maximum.
If D=0, then the test gives no information regarding the point.

Answer 2

so the answer would be...

Answer 3

There's only one critical point which is a minimum, namely, f(1,3)=1.