+1993 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 ?
+36916 https://web2.0calc.com/questions/1-what-is-the-upper-bound-of-the-function
+1993 Cphil, isnt here to help me since that link was from earlier but i beilieve the answer is actually 13
+128448 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
+1993 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?
+128448 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
+1993 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
