Definition of the Derivative Part 2

In this lesson, the definition of the derivative is explained as the fundamental notion of Calculus in terms of a limit of the difference quotient and the Cartesian plot of secant lines vs tangent lines to a function. The transcript illustrates how the slope of the secant line approaches the slope of the tangent line as H approaches zero, resulting in a finite number instead of being undefined. The graphical and algebraic interpretations of this concept are also discussed. Overall, this lesson provides a clear understanding of the definition of the derivative and its relationship to secant and tangent lines.

Be able to explain the definition of the derivative (THE fundamental notion of Calculus) in terms of a limit of the difference quotient and more importantly the Cartesian plot of secant lines vs tangent line to a function.

• How can you use a secant line to approximate the slope of a curve at a point?
• How can you make two points on a secant line approach each other?