Slope between Two Points on a Curve

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Calculate the slope between two points on one of three curves by dragging the locators. As the locators get close enough, the slope gets closer to the slope of the tangent line, which is the value of the derivative of the function at the point.

Contributed by: Trevor Cole (March 2011)
Open content licensed under CC BY-NC-SA



The slope between two points, joined in the diagram by an arrow is calculated. The tangent at the point at the base of the arrow is calculated from the derivative of the function. The tangent line is shown in green.

It can be seen with a suitable choice of parameters that:

a straight line has a constant slope, and

the slope between two points approaches the tangent, as the distance between the points decreases.

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