2.4 - Rates of Change and Tangent Lines

Relating tangents and derivatives

• A derivative is an instantaneous rate of change, as opposed to slope/average rate of change, which requires two points
• A way to find the average rate of change of a curve is to find the slope of a secant of the curve (a line intersecting it at two points which we can call $Q$ and $P$)
• As $Q$ approaches $P$, the secant $\overline{PQ}$ approaches a line tangent to the curve (intersecting at one point)
• The smaller the interval, the closer the avg. rate of change is to the instantaneous rate of change
• The slope of the tangent represents the derivative

Basic Derivatives - major part of this section