to the change in $x$ between two points $x_{2}$ and $x_{1}$ and then letting $x_{2} = x_{1}$. Writing the last statement in symbols, we have $$\mbox{slope} =  \frac{y(x_{2})-y(x_{1})}{ x_{2}- x_{1}}
 \label{eq:slope}$$ and then let $x_{2}= x_{1}$. The same procedure should work for any smooth function $y(x)$, but the procedure would become pretty tedious if the function is very complicated, as the next exercises demonstrate.

[**EXERCISE**]{}

[**2.1**]{} Find the slope of the function $y(x) = x^{4}$ at the point $x=x_{1}$ using the method of Eq. \[eq:slope\]. Show all your work. Hint: (Check your result by noting that when $x_{1} = 3$ the value of the slope is 108.)

[**2.2**]{} You are running around a circular quarter-mile track. The coach tells you that your distance from the starting line is increasing proportionally to the cube of the time. At the end of 1 second you have traveled 3 m.\
(a) Write an equation for $s(t)$, the distance traveled, as a function of $t$. Check your equation by noting that you must have traveled 24 m at the end of 2 seconds.\
(b) Your speed at any time $t$ is the rate of change of your distance at time $t$.\
Find your speed 