User Name Remember Me? Password

 Calculus Calculus Math Forum

 September 9th, 2017, 06:31 PM #1 Senior Member   Joined: Apr 2017 From: New York Posts: 162 Thanks: 6 Intermediate Value Theorem question: Is there a number that is exactly 5 more than its cube? What I tried : x=number x+5=x^3 if we rearrange: x^3-x-5 after here I think I need to plug in two consequent numbers?(how do I pick that two numbers?) to see x^3-x-5<0 and x^3-x-5>0 and? September 9th, 2017, 06:33 PM #2 Senior Member   Joined: Aug 2012 Posts: 2,409 Thanks: 753 Try 0 and a trillion. How'd I guess those? You can see that for x near 0, the -5 predominates. And for x large, the x^3 predominates. But even x = 2 works since 2^3 - 2 = 6. September 10th, 2017, 04:12 AM   #3
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Quote:
 Originally Posted by Leonardox question: Is there a number that is exactly 5 more than its cube? What I tried : x=number x+5=x^3 if we rearrange: x^3-x-5
You've lost the "=". You should have x^3- x- 5= 0.

Quote:
 after here I think I need to plug in two consequent numbers?(how do I pick that two numbers?) to see x^3-x-5<0 and x^3-x-5>0 and?
What do you mean by "consequent" here? If you are thinking they must be successive integers, n and n+1, that is not correct. It is not hard to see that if x= 0, 0^3- 0- 5= -5< 0 and that if x=2, 2^3- 2- 5= 8- 2- 5= 1> 0.

How do you pick them? 0 is always an easy first choice, then "guess and check"! September 10th, 2017, 10:11 AM   #4
Global Moderator

Joined: Dec 2006

Posts: 21,026
Thanks: 2257

Quote:
 Originally Posted by Leonardox Is there a number that is exactly 5 more than its cube?
Yes. It's close to -1.904160859 as -1.904160859³ + 5 = -1.90416086 approximately. September 10th, 2017, 12:14 PM #5 Member   Joined: May 2017 From: Russia Posts: 34 Thanks: 5 $\displaystyle x^3-x-5$ has a real root because of its odd degree. Tags intermediate, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post deadweight Calculus 3 September 12th, 2015 03:47 AM jiasyuen Calculus 3 January 5th, 2015 05:11 AM nubshat Calculus 1 October 23rd, 2013 12:32 AM chris123 Real Analysis 0 February 21st, 2013 05:44 PM Twoxsmart Calculus 1 January 28th, 2009 09:55 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      