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Tangent Line & Slope of a Curve at a Point

1. A secant can be used to estimate the slope of the curve at a point (or the tangent line slope). Drag the red point "1+h" to move point B closer to point A. What Value does the slope of the secant approach?

2. Use the buttons at the top to extend the green secant. Again drag the "1+h" point to get another look at what happens to the secant as h gets small.

3. Drag "1 + h" so that the length of the blue line gets very small. What happens to the length of the red line on the y-axis. Will the red line ever get as small as the blue line? What happens to the ratios of these lengths? What do these ratios represent (hint: the value of the ratio is already calculated for you)?

4. When you move point B the secant slope changes but not the tangent slope. Why?

5. Why is the slope of the secant undefined when you trace to h = 0?