Name:
Mods:
Date:
Mean Value Theorem
GeoGebra Project
Complete this worksheet and turn in this worksheet by ________ using your chromebooks at
home. This will be a 10 point assignment. Answer everything in bold.
Example 1: Follow this link: http://tube.geogebra.org/student/m412325
A. Click on the boxes for “show tangent” and “show c.”
B. Drag point c until the tangent line is parallel to the secant line (make sure that c is
between a and b).
C. The value of c is ____________
*Notice that “c” is the x value in which the instantaneous rate of change is equal to the
average rate of change in the given interval [3, 7].
Example 2:
A. Drag the sliders for a and b to a = 4 and b = 8.
B. Drag point c until the tangent line is parallel to the secant line ( mtan = msec )
*make sure that c is between a and b.
C. The value of c is _____________
D. What did you just find? (Hint: look at example 1)
Example 3: Follow this link: http://tube.geogebra.org/student/m412329
A. Click on the boxes for “show tangent” and “show c.” Drag the sliders until a=1 and b=8.
B. Try to drag c until the tangent line is parallel to the secant line( mtan = msec )
make sure that c is between a and b.
C. What is different about this function that makes this impossible?
D. Try to find values of a and b that you can get a tangent line parallel to the secant line
(make sure that c is between a and b). What values of a and b did you find? How
does this relate to part C?
Example 4: Follow this link: http://tube.geogebra.org/student/m412339
A. Click on the boxes for “show tangent” and “show c.”
B. How many values of c can you find that give you a tangent line parallel to the secant
line? What are these c value?
C. Move you sliders to a = 4 and b = 6. How many values of c (between a and b) can you
find that give you a tangent line parallel to the secant line?
D. Explain why we do not use the MVT to find c when there is a graph such as this one.