Chapter 8.5, Problem 29P

To determine

(a)

To calculate:

The value of k if the point $\left(0,0\right)$ is a saddle point. The function is $f\left(x,y\right)=x^3-k{y}^2-5xy$.

To determine

(b)

To calculate:

The value of k if the point $\left(0,0\right)$ is a local maximum. The function is $f\left(x,y\right)=x^3-k{y}^2-5xy$.

To determine

(c)

To calculate:

The value of k if the point $\left(0,0\right)$ is a local minimum. The function is $f\left(x,y\right)=x^3-k{y}^2-5xy$.