Chapter 4.2, Problem 71E

To determine

(a) To show that F depends only on the ratio $\left[\frac{v_2}{v_1}\right]$ and is equal to $F(r)=\left[\frac{1}{2}\right]\left(1-r^2\right)\left(1+r\right)$ where, $0\le r\le 1$ the maximum and minimum values of the function $y=x^3-24\ln x$ on the interval by comparing values at the critical points and end points.

(b) To show that maximum value of F(r) = 0.59

(c) To explain why Betz formula for F(r) is not meaningful for r close to zero.