The Mean Value Theorem Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) 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   
    

(2) Find the value(s) of that satisfy the equation for in the conclusion of the Mean Value Theorem on

(3) Find the value(s) of that satisfy the equation for in the conclusion of the Mean Value Theorem on

(4) Does the function satisfy the hypotheses of the Mean Value Theorem on the interval State why or why not.

(5)  Does the function satisfy the hypotheses of the Mean Value Theorem on the interval State why or why not.

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

(7) Show that a cubic can have at most three zeros.

(8) Show that the function has exactly one zero in the interval

(9) Show that the function has exactly one zero in the interval

(10) Suppose that and that for all Must for all Why or why not?

(11) Suppose that for all Find if

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

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

    (a)         (b) when
    

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

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The Mean Value Theorem Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/the-mean-value-theorem-homework.html