Visualizing Tangent Lines

Overview

• It is hard to define the slope for a function that is not a line.
• A tangent line is the line approximating \(f(x)\) at a single numerical value of $x$, called $a$.
• We know from algebra how to find and interpret the slope of this line.

This interactive lets you move the graph of a tangent along a function, and see what the the changing tangent line tells us about the original function.

Instructions

• Use the slider to choose a value of \(a\).
• The image displays the graph of \(f(x)\), the point \((a,f(a))\), and the tangent line at that point.
• As you move the slider, watch use the slope of the the tangent line to describe the the non-linear function.