Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,459 questions

17,854 answers

1,446 comments

811,114 users

Determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

0 votes

Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

asked Jan 29, 2015 in CALCULUS by anonymous

2 Answers

0 votes

Step 1:

The function is .

Consider .

Derivative on each side by .

Apply the power rule of derivative :.

Step 2:

To examine the behavior of a function, equate the derivative to zero.

The x values are .

answered Jan 31, 2015 by james Pupil
edited Jan 31, 2015 by yamin_math
0 votes

Step 3:

The function is .

The domain of the function is image.

There are four regions to examine the behavior of the function.

First region  image.

Consider a test point in the region.

The derivative is negative, the function is decreasing over image.

Second region  image.

Consider a test point image in the region.

The derivative is positive, the function is increasing over image.

Third region  image.

Consider a test point image in the region.

image

The derivative is negative, the function is decreasing over image.

Fourth region  image.

Consider a test point image in the region.

image

The derivative is positive, the function is increasing over image.

A monotonic function is increasing over image and image.

A monotonic function is decreasing over image and image.

Therefore the function is not strictly monotonic.

Solution :

The function is not strictly monotonic.

answered Jan 31, 2015 by james Pupil
edited Jan 31, 2015 by james

Related questions

asked Jan 27, 2015 in CALCULUS by anonymous
...