Chapter 14.8, Problem 39E

To determine

a. The proof of $L={\left(h^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+b^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ by using Lagrange multipliers(Figure 21).

b. The value of L is also equal to the radius of the circle with center $\left(-b,-h\right)$ that is tangent to the graph of $xy=bh$.