Calculus Not by Hand

Calculate slope using small change in $x$

Look at the following graph, which has a new line marked on it. It isn’t a tangent because it doesn’t touch the curve only at a single point. But it does seem to be centered around time $3$ minutes in some way.

In fact, there is connection to a time of $3$ minutes. What we’ve done is chosen a time above and below this point of interest at $t=3$. Here, we’ve selected points $2$ minutes above and below $t=3$ minutes. That is, $t=1$ and $t=5$ minutes.

Using our mathematical notation, we say we have a $\Delta x$ of $2$ minutes. And we have chosen points $x- \Delta x$ ...