2.6. Slope of a Tangent Line and the Definition of the Derivative

• This section includes the slope of a tangent line and the definition of the derivative, and the equations for a tangent line, a secant line, and a normal line.

• In the graph of a function, the slope of a line drawn tangent to the curve through some point (a,f(a)) on the curve is the derivative of the function at point (a,f(a)). In other words, the slope of the tangent at point (a,f(a)) equals the derivative f′(a) at that point. (If a tangent line is vertical, its slope is undefined.) The slope of a tangent at a point measures the change in the curve at that point.