Still celebrating National IT Professionals Day with 3 months of free Premium Membership. Use Code ITDAY17

x
Solved

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

Posted on 2014-11-22
Medium Priority
201 Views
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
Question by:naseeam
[X]
###### Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points

LVL 84

Assisted Solution

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

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

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

LVL 1

Author Comment

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

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 59

Expert Comment

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 84

Expert Comment

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

## Featured Post

Question has a verified solution.

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

This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
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…
###### Suggested Courses
Course of the Month5 days, 6 hours left to enroll