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the slope of a curve

What is the slope of a curve? Look at the graph of y = x2. Draw lines on the curve to represent a slope of -10, -1, 0, 1, and 10.



Examine the slope between two points on the graph that are very close together. For example, at x = 2, you may want to look at the slope between 1.99 and 2.01. Repeat this process at various parts of the graph. Describe the relationship between the x-coordinate you center on and the slope you find.

 Related External Resources

Algebra and Calculus Sketches
These Geometer's SketchPad files can be used to show the transformation of a secant line into a tangent line as the points shared by the parabola and the line become closer.

Linear Functions Tangent to their Product
This exploration asks you to find a curve that is tangent to a product of two other curves.

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