Chapter 14.8, Problem 16E

To determine

We need to

a. Show that there is a unique point $P=\left(a,b\right)$ on $g\left(x,y\right)=1$ where $\nabla f_p=\lambda \nabla g_p$ for some scalar $\lambda$.

b. Refer to figure 14 to determine whether $f\left(P\right)$ is a local minimum or a local maximum of f subject to the constraint.

c. Does figure 14 suggest that $f\left(P\right)$ is a global extremum subject to the constraint?