Monotonic Functions 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) What are the critical points of given . On what intervals is increasing or decreasing? At what points, if any, does assume local maximum and minimum values?

(2) What are the critical points of given . On what intervals is increasing or decreasing? At what points, if any, does assume local maximum and minimum values?

(3) What are the critical points of given . On what intervals is increasing or decreasing? At what points, if any, does assume local maximum and minimum values?

(4) Given find the intervals on which the function is increasing and decreasing. Then identify the function's local extreme values, if any, saying where they are taken on. Which, if any, of the extreme values are absolute? Support your finding with a graph of the function.

(5) Given find the intervals on which the function is increasing and decreasing. Then identify the function's local extreme values, if any, saying where they are taken on. Which, if any, of the extreme values are absolute? Support your finding with a graph of the function.

(6) Given find the intervals on which the function is increasing and decreasing. Then identify the function's local extreme values, if any, saying where they are taken on. Which, if any, of the extreme values are absolute? Support your finding with a graph of the function.

(7) Given find the intervals on which the function is increasing and decreasing. Then identify the function's local extreme values, if any, saying where they are taken on. Which, if any, of the extreme values are absolute? Support your finding with a graph of the function.

(8) Given find the intervals on which the function is increasing and decreasing. Then identify the function's local extreme values, if any, saying where they are taken on. Which, if any, of the extreme values are absolute? Support your finding with a graph of the function.

(9) Given find the intervals on which the function is increasing and decreasing. Then identify the function's local extreme values, if any, saying where they are taken on. Which, if any, of the extreme values are absolute? Support your finding with a graph of the function.

(10) Given find the intervals on which the function is increasing and decreasing. Then identify the function's local extreme values, if any, saying where they are taken on. Which, if any, of the extreme values are absolute? Support your finding with a graph of the function.

(11) Identify the function's local extreme values for in the given domain of and say where they are assumed. Which of the extreme values, if any, are absolute? Support your finding with a graph of the function.  

(12) Identify the function's local extreme values for in the given domain of and say where they are assumed. Which of the extreme values, if any, are absolute? Support your finding with a graph of the function.  

(13) Identify the function's local extreme values for in the given domain of and say where they are assumed. Which of the extreme values, if any, are absolute? Support your finding with a graph of the function.  

(14) Sketch the graph of a differentiable function through the point if and

    (a) for and for
    
    (b) for and for

    (c) for

    (d) for
    

(15) Sketch the graph of a differentiable function that has

    (a) a local minimum at and a local maximum at
    
    (b) a local maximum at and a local minimum at

    (c) a local maximum at and a local maximum at

    (d) a local minimum at and a local minimum at
    

(16) Sketch the graph of a continuous function such that

    (a) for all as and   as
    
    (b) for all as and   as
    

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Monotonic Functions Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/monotonic-functions-homework.html