Quiz (The Mean Value Theorem)

Show all work and justify each step.

(1) Show that the following equations have exactly one real root.
    
    (a)         (b)

(2) Determine the values of the constants and such that the following functions satisfies the hypotheses of the Mean Value Theorem on the given interval.

    (a)   on   

    (b)   on   
    

(3) Use the Mean Value Theorem to show the following

    (a)         (b) when
    

(4) Let Prove that for any interval the value of guaranteed by the Mean Value Theorem is the midpoint of the interval.

(5) Let and Show that for all in their domains. Can we conclude that is constant?

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Cite this as:
Mean Value Theorem Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/mean-value-theorem-quiz.html