introduction, as measuring the rate of change of a quantity. We deal with quantities that can be represented by curves on a graph. Our problem is to find the rate of change of the quantity at a point on the graph. That rate of change is measured by the slope of the tangent at the point to the curve representing the function.

In what follows, I shall introduce a quantity, that I call a “dibbl”, so small that its square “is as good as” zero - practically, it is zero - and if it is zero, why not say so? The dibbl will make it easier for us to calculate slopes.

NEW LANGUAGE
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I show, in this Section, how to find the slopes of functions that can be described by integer powers of an independent variable. The problem is to find the equation of a straight line that is tangent to the function at some point. Once we know that equation we can just read off the slope of the line.

Let’s try to find the slope of the tangent at some point, call it $x_{1}$, of the quadratic equation $y(x) = cx^{2}$ where $c$ is some constant. Then 