Extreme Values 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) Find the critical numbers of the given functions.

(2) Find the absolute maximum and minimum values of the function on the interval . Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.

(3) Find the absolute maximum and minimum values of the function on the interval . Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.

(4) Find the absolute maximum and minimum values of the function on the interval . Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.

(5) Find the absolute maximum and minimum values of the function on the interval . Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.

(6) Find the absolute maximum and minimum values of the function on the interval . Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.

(7) Find the absolute maximum and minimum values of the function on the interval . Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.

(8) Find the absolute maximum and minimum values of the function on the interval . Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.

(9) Find the absolute maximum and absolute minimum values of the given function on the given interval.

(10) Find the extreme values of the function and where they occur.

(11) Find the extreme values of the function and where they occur.

(12) Find the extreme values of the function and where they occur.

(13) Find the extreme values of the function and where they occur.

(14) Find the extreme values of the function and where they occur.

(15) Find the derivative at each critical point and determine the local extreme values for the function

(16) Find the derivative at each critical point and determine the local extreme values for the function

(17) Find the derivative at each critical point and determine the local extreme values for the function

(18) Let Does exist? Does exist? Does exist? Determine all extrema of

(19) What is the largest possible area for a right triangle whose hypotenuse is long?

(20) The height of a body moving vertically is given by with in meters and in seconds. Find the body's maximum height.

(21) Show that is a critical number of the function but does not have a relative extremum at

(22) Consider the cubic function where Show that can have zero, one, or two critical numbers and give examples of each.

(23) Explain why the function must attain a minimum in the open interval

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Extreme Values Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/extreme-values-homework.html