Secant Lines and Tangent Lines (Calculus 1)

This Calculus 1 video explains the difference between a secant line and tangent line. We talk about secant lines and average rate of change vs tangent lines and instantaneous rate of change. We show how looking over shorter and shorter intervals gets us closer to knowing the slope of a tangent line. We explain different versions of the slope formula, using functions. And finally, we look at a secant line to tangent line animation and how the limit of the difference quotient becomes the formula for a slope function, which we call the limit definition of the derivative.
0:00 Secant lines
2:04 Finding average rate of change
3:55 Tangent lines & instantaneous rates
4:59 Building the difference quotient
7:53 Secant line to tangent line animation
8:23 Limit definition of derivative
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