Sorry, this page requires a Java-compatible web browser.

Tangent Line & Slope of a Curve at a Point

Drag the dot "x" to move the points on the parabola and the tangent line.

Questions

1. Drag the x-value to 1.8. The points on the curve & the tangent line seem to merge. Are they in exactly the same location?

2. Drag the x-value to 2. Why does the "slope of secant" say "undefined"?

3. Compare the slope of the secant line to the slope of the tangent line? Is the secant line slope always greater, never greater, or depends?

4. For which x-values does the secant line & the section of the curve between the two points appear to merge with the tangent line? Why do they all look the same?