Chapter 4.1, Problem 102E

Market Share: Smartphones The following graph shows the approximate market shares, in percentage points, of smartphones using apple’s iOS operating system and Microsoft’s Windows Phone operating system, from the second quarter of 2011 to 2014. (t is time in years and $t=0$ represents the second quarter of 2010.)

Market share (%)

Le t $I\left(t\right)$ be the iOS market share at time t, and let $W\left(t\right)$ be the Windows Phone market share at time t.

a. What does the function $I-W$

measure? What does its derivative $\left(I-W\right)\text{'}$

measure?

Android:	$A\left(t\right)=3.0t^3-29t^2+100t-38$
$\text{iOS:}$	$I\left(t\right)=-2.3t+21.$

b. The graph suggests that, On the interval $\left[1,4\right],I-W$

is

(A) increasing..

(B) decreasing.

(C) increasing the decreasing.

(D) decreasing, then increasing.

c. The two market shares are approximated by

$\text{iOS:}$	$I\left(t\right)=0.7t^3-5.2t^2+8.9t+14$
$\text{Windows Phone:}$	$W\left(t\right)=-0.7t^2+3.9t-2.$

Compute $\left(I-W\right)\text{'}$, starting its unit of measurement. On the interval $\left[1,4\right],\left(I-W\right)\text{'}$ is (A) positive.

(B) negative.

(C) positive, then negative.

(D) negative, then positive.

How is this behavior reflected in the graph, and what does it mean about the market shares of the iOS and Windows Phone operating systems?

b. Compute $\left(I-W\right)\text{'}\left(2\right)$. Interpret your answer.