Chapter 13 Project

Rideshare Function

A certain rideshare company charges $\mathrm{\$}3.00$ to pick up a passenger and an additional $\mathrm{\$}0.90$ for each mile or fraction of a mile that the passenger is driven.

1. Graph a function $C\left(x\right)$ that reflects the cost to a passenger for a ride of x miles over the x-interval $\left[0,5\right]$.

2. Find and classify all points of discontinuity of the function C.

3. If it exists, determine $\underset{x\to 1.7}{\lim }C\left(x\right)$. If the limit does not exist, determine the one-sided limits, if possible.

4. If it exists, determine limx $\underset{x\to 2}{\lim }C\left(x\right)$. If the limit does not exist, determine the one-sided limits, if possible.

5. If it exists, determine $C^{\prime }\left(1.7\right)$.

6. Is $C^{\prime }\left(x\right)$ defined for every nonnegative x? If not, where is $C^{\prime }\left(x\right)$ not defined?

7. What is the first interval of distance over which a passenger can ride and pay their fare in dollars with no change necessary? How much will the fare be?