Chapter 4.1, Problem 101E

(a)

To determine

The measure of function $A-I$ and derivative $\left(A-I\right)\text{'}$, where functions $A\left(t\right)\text{ and }I\left(t\right)$ represents Android share market and iOS share market at time t.

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

(b)

To determine

The function $A-I$ in interval $\left[1,4\right]$ is,

(A) increasing.

(B) decreasing.

(C) increasing, then decreasing.

(D) decreasing, then increasing

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

(c)

To determine

To calculate: The derivative $\left(A-I\right)\text{'}$ stating its unit, where functions $A\left(t\right)=3.0t^3-29t^2+100t-38$ and $I\left(t\right)=-2.3t+21$ represents function of Android share market and iOS share market at time t respectively. The following graph shows the market share, in percentage point, of smartphones using Google’s Android and Apple’s iOS operating system.

Also choose the appropriate option representing $\left(A-I\right)\text{'}$ 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 Android share market and iOS share market, and how is this behavior reflected in the provided graph.

(d)

To determine

To calculate: The derivative $\left(A-I\right)\text{'}$ at $t=3$, where functions $A\left(t\right)=3.0t^3-29t^2+100t-38$ and $I\left(t\right)=-2.3t+21$ represents function of Android share market and iOS share market at time t respectively.

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