Secant Line

This illustrates the slope of a secant line on a curve. The play button advances the construction. Step 1 - Shows the graph of the function , and a point A on the curve. The point may be moved along the curve. Step 2 - A point B is added to the right of point A. The x distance between the points can be controlled with the slider. Left and right arrow keys can fine set the slider. Step 3 - Draws a purple dashed secant line through the two points. Step 4 - Calculates the slope of the line through the two points. Step 5 - Shows a pink tangent line and the slope of the tangent line.
Observations to make: At step 2, adjust the slider and observe how point B varies for a few locations of point A. At step 3, notice how the slope of the line varies as h is decreased. At step 4, notice how the slope changes as h is decreased. What happens when h is set to 0? Compare the value of the slope and the x value of point A. Do you see a relationship? At step 5, compare the slope of the red dashed tangent line and the slope of the purple short dashed secant line. What happens as h is decreased?