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 ?

jjennylove Sep 12, 2019

#1**0 **

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

ElectricPavlov Sep 12, 2019

#2**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

#4**+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

CPhill Sep 12, 2019

#5**+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**+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

CPhill
Sep 12, 2019

#7**+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