at any time $t$. (Here we are writing just $t$, instead of $t_{1}$).\
(c). A horse can gallop with a top speed of about 7 m/sec. After how many seconds are you running at a horse’s top speed?\
(d) Did you have to consider the shape of the track when you answered (a) through (c)?\

It turns out that we can simplify the calculation of slope by taking the points $x_{2}$ and $x_{1}$ to be very close together. This makes sense, because at the end of the calculation we are going to let $x_{2} = x_{1}$. So let’s start by simplifying the notation, dropping the subscripts and restating the problem as follows: [**Find the slope of the function $y(x)$ at some value of $x$.**]{}

We will do this by finding the slope of a straight line that intersects $y(x)$ at two points that are so close together that they are [**practically, but not quite, the same point**]{}. We write the two points as $y(x)$ and $y(x+dx)$. Since $x$ and $x+dx$ are nearly the same, we say that $x+dx$ is just a [*[dibbl]{}*]{} away from $x$.

Also, since we know that $y(x)$ is described by a smooth curve, we also know 