Go Premium for a chance to win a PS4. Enter to Win

x
?
Solved

How to find absolute extrema of  4 - abs(t - 4)

Posted on 2014-11-22
8
Medium Priority
?
206 Views
Last Modified: 2014-11-24
Determine the absolute extrema of the function and the x-value in the closed interval where it occurs.

h ( t )  =  4  -   abs ( t - 4 )      
closed interval is  [ 1, 6 ]

This is not a homework problem.  

This problem is from high school Advance Placement Calculus class.
0
Comment
Question by:naseeam
7 Comments
 
LVL 85

Assisted Solution

by:ozo
ozo earned 200 total points
ID: 40460203
an extrema of a continuous function is either where the derivative changes sign or at the endpoints of the domain
0
 
LVL 27

Assisted Solution

by:d-glitch
d-glitch earned 400 total points
ID: 40460215
You should plot the function.  Try the integers in the range of interest.
Do you know what the plot of abs(t) looks like?  It is always GTE zero.
So what does 4 abs( ) look like?
0
 
LVL 32

Accepted Solution

by:
phoffric earned 1400 total points
ID: 40460283
I would break the closed interval of [1, 6 ] into two partitions: one where t - 4 >= 0 and one where t - 4 < 0. Now you have two different functions h1(t) and h2(t), one for each partition with no abs() function involved. Removing the abs() function usually makes these problems easier to understand. Analyze absolute extrema on both partitions, which should be easy.

I assume that you mean "the t-value" rather than "the x-value".
0
Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 
LVL 1

Author Comment

by:naseeam
ID: 40460836
h1(t) = 4 - ( t - 4 ) ;        [4, 6 ]
h2(t) = 4 - ( - t  +  4);     [1, 4 ]

h1 ' ( t )  =  - 1
h2 ' ( t ) =  1

At t = 4, slope is undefined.  There is absolute maximum at t = 4.

Am I correct ?
0
 
LVL 32

Expert Comment

by:phoffric
ID: 40460854
I hoped you first simplified h1(t) and h2(t).
You are correct.

In general, as you progress into harder functions and inequality relationships with multiple absolute value functions, the task first becomes identifying multiple partitions and then defining functions on each partition having no absolute value functions. A bit harder than this problem if the individual regions for different absolute value expressions overlap.
0
 
LVL 61

Expert Comment

by:HainKurt
ID: 40461224
strange.. I remember I posted something here, but I dont see now... did someone delete my post?

I dont see my post but i still get notifications? what happened to my post (and possible points)?
0
 
LVL 85

Expert Comment

by:ozo
ID: 40461588
each partition having no absolute value functions
or more generally, each partition being monotonic.
0

Featured Post

How to Use the Help Bell

Need to boost the visibility of your question for solutions? Use the Experts Exchange Help Bell to confirm priority levels and contact subject-matter experts for question attention.  Check out this how-to article for more information.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
This article covers the basics of data encryption, what it is, how it works, and why it's important. If you've ever wondered what goes on when you "encrypt" data, you can look here to build a good foundation for your personal learning.
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

876 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question