Two key interpretations of the derivative are as instanenous rates of change and as the slopes of tangent lines. I introduced our subject to these two interpretations way back in my Introduction to Limits 1 - before we even had formal notation for them! Section 2.2 of APEX Calculus 1
shows how to make these precise now that we know about limits and derivatives.
Module Learning Objectives.
Write out the equation of a line in general
Write out the equation of a tangent line
Video2.2.1.Review: Equations of Lines.
The first half of this video is a careful review of the precalculus concept of finding an equation of a line. The second half then uses calculus to find the slope.