Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 11

a.) The graph of the distance as a function of time of a particle is shown below suppose that it starts moving to the
right along a horizontal line. When is the particle moving to the right? Moving to the left? Standing still?








$
\begin{array}{|c|c|c|}
\hline\\
\text{Right} & \text{Left} & \text{Standing Still}\\
\hline\\
0 < t < 1 & 2 < t < 3 & 1 < t < 2\\
\text{and} & & \text{and}\\
4 < t < 6 & & 3 < t < 4\\
& & \\
\hline
\end{array}
$


b.) Draw the graph of the velocity function.



The graph is obtained by evaluating the slopes of the curve in the intervals given in part(a) using point slope form.
For example @ $0 < t < 1$
$\displaystyle \text{Velocity } = m = \frac{3-0}{1-0} = 3$