Chapter 11.1, Problem 102E

(a)

To determine

The measure of function $I-W$ and derivative ${\left(I-W\right)}^{\prime }$, where functions $I\left(t\right)\text{ and }W\left(t\right)$ represents iOS share market and Windows phone market at time t.

The following graph shows the market share, in percentage point, of smartphones using Apple’s iOS operating system and Microsoft’s Windows phone operating system.

(b)

To determine

Whether the function $I-W$ in interval $\left[1,4\right]$ is,

(A) increasing.

(B) decreasing.

(C) increasing, then decreasing.

(D) decreasing, then increasing

Where, function s $I\left(t\right)\text{ and }W\left(t\right)$ represents iOS share market and Window’s market share at time t. The following graph shows the market share, in percentage point, of smartphones using Apple’s iOS operating system and Microsoft’s Windows operating system.

(c)

To determine

To calculate: The derivative of ${\left(I-W\right)}^{\prime }$ and states its unit, where the functions $I\left(t\right)=0.7t^3-5.2t^2+8.9t+14$ and $W\left(t\right)=-0.7t^2+3.9t-2$ represents function of iOS share market and Window’s phone market share at time t respectively.

The following graph shows the market share, in percentage point, of smartphones using Apple’s iOS operating system and Window’s Phone operating system.

Also choose the appropriate option representing ${\left(I-W\right)}^{\prime }$ in the interval $\left[1,4\right]$ from the following:

(A) positive.

(B) negative.

(C) positive, then negative.

(D) negative, then positive.

Give the interpretation about the iOS share market and Window’s phone share market, and how is this behavior reflected in the provided graph.

(d)

To determine

To calculate: The derivative ${\left(I-W\right)}^{\prime }$ at $t=2$, where functions $I\left(t\right)=0.7t^3-5.2t^2+8.9t+14$ and $W\left(t\right)=-0.7t^2+3.9t-2$ represents function of iOS share market and Window’s phone market share at time t respectively.

The following graph shows the market share, in percentage point, of smartphones using Apple’s iOS operating system and Window’s Phone operating system.

Also, interpret the answer.