Chapter 4.6, Problem 74E

To determine

(a)

To prove if $\underset{x\to -\infty }{\lim }R(x)=0$ and $\underset{x\to \infty }{\lim }R(x)=M$, therefore $R=0$ and $R=M$ are horizontal asymptotes of $R$.

To determine

(b)

It is to verify that, $R$ is increasing for all $x$.

To determine

(c)

There is only one inflection point of $R$, and value of R at inflection point is $\frac{M}{2}$. To the left of it $R$ is concave up and to the right of it $R$ is concave down.