Chapter 3.2, Problem 64E

Refer to Exercise 61.

What was the maximum value of the company during the first $6$ months since it went public, and when was that maximum value attained?

Assuming that the value of one share will continue to increase at the rate that it did during the period following the $6$ th month, what is the limit of the total value of the company as $t$ increases?

Effect of Stocks on Total Assets of a Company After a computer software company went public, the price of one share of its stock fluctuated according to the graph in Fig1 (a). the total worth of the company depended on the value of one share and was estimated to be

$W\left(x\right)=10\frac{12+8x}{3+x}$,

Where $x$ is the value of one share (in dollars) and $W\left(x\right)$ is the total value of the company in millions of dollars. [See Fig.1 (b).]

Find the total value of the company when $t=1.5$ and $t=3.5$.

Find ${\frac{dx}{dt}|}_{t=1.5}$ and ${\frac{dx}{d{t}_{}}|}_{t=3.5}$. Give an interpretation for these values.