The Mean Value Theorum
G. Battaly, Calculus I, Westchester
Community College
The
blue curve below is a cubic function. Consider the interval [a, b] to be [0.5, 6.74]
The cubic function is: 1. continuous on the closed interval [0.5, 6.74] and
2. differentiable on the open interval (0.5, 6.74)
The objects in green relate to the secant line connecting the endpoints of the interval.
msec is the slope of the secant line.
The objects in red relate to the tangent line at the point C on the cubic function along the interval.
mtan is the slope of the tangent line
xcoordinate is the x coordinate of the point C
Click and drag the slider to change the location of point C. Move the slider until the value of mtan equals msec
(to the nerest tenth)
Other slider options: 1. Click on the
slider and then use the right or left arrow to fine-tune the position. 2.
Right click on the slider and select 'animation on' for automatic movement.
1. How are the secant and tangent lines aligned when mtan =
msec? ____________________
2.
At how many locations on the interval does mtan = msec? _______
3.
How many locations on the interval, with mtan = msec, are guaranteed by the Mean Value Theorum? ______
4.
Does the Mean Value Theorum apply for all polynomials on any interval? ______
5.
Does the Mean Value Theorum apply for all continuous functions on any interval? ______
Explain. __________________________________________________
G Battaly, Calc I, WCC, 2014
G. Battaly, Math Department, Westchester Community College, Created with GeoGebra
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