Chapter 3.2, Problem 62E

Refer to Exercise 61. Use chain rule to find ${\frac{dW}{dt}|}_{t=1.5}$ and ${\frac{dW}{dt}|}_{t=3.5}$. Give the interpretation for these values.

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.