Chapter 13.8, Problem 37E

(a)

To determine

To calculate: The critical points for the function $f\left(x,y\right)={\left(x-1\right)}^2{\left(y+4\right)}^2$.

(b)

To determine

To calculate: The relative extrema for the function $f\left(x,y\right)={\left(x-1\right)}^2{\left(y+4\right)}^2$.

(c)

To determine

To calculate: The points for which the second partials test for the function $f\left(x,y\right)={\left(x-1\right)}^2{\left(y+4\right)}^2$ fails.

(d)

To determine

To graph: The function $f\left(x,y\right)={\left(x-1\right)}^2{\left(y+4\right)}^2$ along with the extrema and saddle points.