The average high temperature in Valerie's city during the month of December is 50°F.
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Compute the gradient of .
Set this equal to the zero vector and solve for the critical points.
The last case has no real solution, so we can ignore it.
Now,
so we have two critical points (0, 0) and (2, 2).
Compute the Hessian matrix (i.e. Jacobian of the gradient).
Check the sign of the determinant of the Hessian at each of the critical points.
which indicates a saddle point at (0, 0);
We also have , which together indicate a local minimum at (2, 2).