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Cubic Function

An interesting property of a cubic function with 3 x-intercepts: a tangent line at the average of two intercepts passes through the third.

Turn on the axes and sketch a cubic which crosses the x-axis 3 times.

Enter its equation as k*(x-a)*(x-b)*(x-c)

Picture 1

Place a point on the curve and set its location to be (a+b)/2

Picture 2

Create the tangent at this point

Picture 3

Construct the intersection between the tangent and the x-axis.

Picture 4

Use the Symbolic Panel to get the coordinates of point B.

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