Chapter 5.2, Problem 52E

To determine

(a)

To check:

The $C\left(x\right)=0$ when,

$x=\frac{\ln \left(A/R\right)}{1/a-1/r}$

An alternative form of cohesiveness (see the previous exercise) is given by

$C\left(x\right)=R{e}^{-x/r}-A{e}^{-x/a}$

Suppose that $R>A$ and $r<a$

To determine

(b)

To check:

The $C\left(x\right)$ has relative minimum when $x=\frac{\ln \left(rA/aR\right)}{1/a-1/r}$.

To determine

(c)

To find:

The values of $x$ for which $C\left(x\right)=0$ and the value for which $C\left(x\right)$ has a relative minimum.

$R=5$, $A=3$, $r=\frac{1}{5}$ and $a=\frac{1}{2}$