Tangents and Secants

Tangent and Secants. Use this applet to explore the gradients of secants and tangents of the graph of If you would like to see a definition of secant and tangent please go to http://www.mathsisfun.com/definitions/secant-line-.html
1. Click and drag point B towards point A. Notice what happens to the gradient of the secant. 2. What value does the gradient tend towards as B gets closer to A? 3. Now click on the tangent button in the left hand menu. This shows the tangent at point A. What is the gradient of the tangent? 4. Now move point A to (2, 4) and repeat steps 1 - 3. 5. Now move point A to (3, 9) and repeat steps 1 - 3. 6. Can you state a rule that connects the gradient of the tangent and the x-coordinate of A for ? 7. This investigation can be extended by changing the function. e.g. click on the Conic function c and change to