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1.What is the upper bound of the function?

f(x)=4x^4−25x^2−5x−13

Enter your answer in the box.

upper bound =

 

wouldnt than answer be just 13 since when you do long divsion  13/4 -25 -5 -13 it is 4 27 346 and 4485 which are all postitive ?

 Sep 12, 2019
edited by jjennylove  Sep 12, 2019
 #1
avatar+18868 
0

https://web2.0calc.com/questions/1-what-is-the-upper-bound-of-the-function

 
 Sep 12, 2019
 #2
avatar+1129 
0

Cphil, isnt here to help me since that link was from earlier but i beilieve the answer is actually 13

 
jjennylove  Sep 12, 2019
 #3
avatar+1129 
0

do you have any ideas?

 
jjennylove  Sep 12, 2019
 #4
avatar+103061 
+2

Divide each term of the polynomial by 4

 

4x^4   - 25x^2  - 5x   - 13

___       _____   ___   ___      =   (1x^4) - ( 25/4)x^2  - (5/4)x - 13/4

 4             4         4        4

 

 

Write down the coefficients    =    1     - 25/4        -5/4      -13/4

 

Drop the first one and remove the minus signs from any of the rest  ....we get ... 25/4     5/4     13/4

 

We have two  possible bounds on the polynomial

 

a)  Take the largest value of the above and add 1  =   25/4 + 1 =  25/4 + 4/4   = 29/4  = 7.25

b)  Take the larger of :  the sum of the coefficients or 1....Add the coefficients = 43/4.....this is greater than 1....so the second possible bound is  43/4  = 10.75

 

Select the smaller  of  (a)  or (b)  =  7.25

 

This tells us that the upper and  lower bounds on zeroes are  7.25   and - 7.25

 

So.....the upper bound  is x = 7.25.....in other words......no real root will be  > 7.25

 

 

 

cool cool cool

 
 Sep 12, 2019
 #5
avatar+1129 
+1

Is it possible for it to be 7 ? Because when I didive 7 by the polyonmial I get all postitive values and that is lower than 7.25?

 
jjennylove  Sep 12, 2019
 #6
avatar+103061 
+1

I don't quite understand what you mean.......we are looking for the possible upper bound on zeroes.....in other words.....we are trying to find the largest x value such that no positive root can exceed this upper bound 

 

Look at the graph here  :  https://www.desmos.com/calculator/omunuy8c4t

 

Note that the largest real root occurs at about (2.68, 0).....so   this confirms the fact that we do not need to search for any real roots  > 7.25 because they do not exist

 

 

cool cool cool

 
CPhill  Sep 12, 2019
 #7
avatar+1129 
+1

https://www.chegg.com/homework-help/explore-cases-0-upper-bound-lower-bound-real-zeros-polynomia-chapter-4.2-problem-69e-solution-9780073519517-exc

 

If you click on this link the upper boun therm states "by using synthetic divsion if alll numbers are postitive and then thats the upper bound "

 

When i solve 7 into the equation so 7/4 -25 -5 -13 , i got all postitive values and then once i do 6 it is a mis of pos and neg values

 
jjennylove  Sep 12, 2019
 #8
avatar+1129 
0

what do you think about that ?

 
jjennylove  Sep 12, 2019

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