For each real number x, let f(x) be the minimum of the numbers 4x+1,

  • Context: Undergrad 
  • Thread starter Thread starter azizlwl
  • Start date Start date
  • Tags Tags
    Minimum Numbers
Click For Summary

Discussion Overview

The discussion revolves around the function f(x), defined as the minimum of the expressions 4x+1, x+2, and -2x+4 for each real number x. Participants are exploring the maximum value of this function, considering the nature of the problem and the range of x.

Discussion Character

  • Exploratory
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asks for the maximum value of f(x) based on its definition.
  • Another participant questions whether the problem is a homework assignment.
  • A later reply clarifies that it is not a homework problem but references a source, "The Advanced Mathematical Thinking," suggesting a reversal tactic for solving it.
  • Several participants inquire about the range of x, questioning if it can be any real number, an integer, or a subset.
  • One participant suggests that the minimum of the functions will vary depending on the subsets of the domain considered and proposes a method to construct a piecewise function based on which expression dominates in different intervals.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the range of x and whether the problem is homework-related. There is no consensus on the maximum value of f(x) or the approach to solving it.

Contextual Notes

Participants note that the solution may depend on the subsets of the domain considered, indicating that different approaches could yield different results.

azizlwl
Messages
1,066
Reaction score
10
For each real number x, let f(x) be the minimum of the numbers 4x+1, x+2, and -2x+4. What is the maximum value of f(x)?
 
Physics news on Phys.org


azizlwl said:
For each real number x, let f(x) be the minimum of the numbers 4x+1, x+2, and -2x+4. What is the maximum value of f(x)?
Is this a homework problem?
 


Mark44 said:
Is this a homework problem?

No, Sir.
It is too taken from The Advanced Mathematical Thinking where the author said it can be solved by reversal tactic.

Sorry if it is incomplete since I copied whatever written in the book.
 


Is there a range for these numbers, i.e., is x any real number, integer, subset of these

or other?
 


Bacle2 said:
Is there a range for these numbers, i.e., is x any real number, integer, subset of these

or other?


http://img214.imageshack.us/img214/5270/35240583.jpg
2.https://www.physicsforums.com/showthread.php?t=632495
http://img850.imageshack.us/img850/1995/68878748.jpg
 
Last edited by a moderator:


Well, the reason I was asking is that , if the minimum of these numbers is done

over different subsets of the line, then the results will be different. The solution

is straightforward: compare the functions and see which of the three dominates

over which part of the domain, and construct a piecewise function: set

f1>f2 ,f1>f3 , f2>f3 , etc., and select, for each interval the smallest.
 

Similar threads

MHB What Is the Minimum Surface Area for a Cuboid Box with a Square Base?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Real Roots of Polynomial Minimization Problem
  • · Replies 1 ·
Replies
1
Views
1K
High School How can hyperreal numbers make infinitesimals logically sound in calculus?
  • · Replies 24 ·
Replies
24
Views
7K
MHB Maximum and minimum of a function
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad ##f(2x)=f^2(x)-2f(x)-1/2## then find ##f(3)##
  • · Replies 17 ·
Replies
17
Views
4K
Undergrad Understanding a proof of inexistence of max nor min
  • · Replies 4 ·
Replies
4
Views
2K
MHB What is the Absolute Minimum Value of f(x)?
  • · Replies 2 ·
Replies
2
Views
2K
MHB What is the Minimum Length of AP + PB?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Maximizing $y=|4x^3+ax^2+bx+c|$ in $[-1,1]$
  • · Replies 1 ·
Replies
1
Views
1K
High School Functions which relate to calculus: Questions about Notation
  • · Replies 36 ·
2
Replies
36
Views
7K