Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.1, Problem 16E

To determine

To find: theextreme values of the function on the interval and where they occur by using analytic method and find critical points that are not stationary points.

Expert Solution & Answer

Answer to Problem 16E

the minimum value is 1 at x=0 and no maximum value exist.

Explanation of Solution

Given information:

The function is g(x)=secx, −π2≤x≤3π2

Calculation: to find the extreme values of function, first find its derivative,

g(x)=secxg'(x)=secx·tanx [differentiate and simplify]

At point x=0 where f'(x)=0 , and the point x=−π2 and x=3π2 , the derivative of function does not exist,

Now substitute in function,

g(x)=secxg(−π2)=−∞ [substitute x=−π2 and simplify]g(3π2)=∞ [substitute x=3π2 and simplify]g(0)=1 [substitute x=0 and simplify]

Thus, the minimum value is 1 at x=0 and no maximum value exist.

Chapter 5.1, Problem 15E

Chapter 5.1, Problem 17E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

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