My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum

LinkBack Thread Tools Display Modes
April 15th, 2013, 10:41 PM   #1
Joined: Apr 2012

Posts: 21
Thanks: 0

Intermediate Value Theorem

Hi all

Strange question here involving the intermediate value theorem.

Consider the equation x^3 + x +e^x = 0

Use the intermediate value theorem to show there is a solution on the interval (-1,0) and show that there is exactly one real solution of the equation.

I've been trying at this one for a couple of hours now and I cant seem to make good headway. My equation fall apart before too long. I have an idea on solving the second half of the question, showing there is exactly on real solution, and that is by graphing it and then possibly trying to manipulate it?

Any help is greatly appreciated. Thank you!
hooperoo is offline  
April 15th, 2013, 11:02 PM   #2
Math Team
agentredlum's Avatar
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 234

Re: Intermediate Value Theorem

It is not as difficult as it may seem, let

So... the y value went from negative to positive... it must have hit zero at least once... that's the intermediate value theorem.

To show it hit zero only once take the derivative,

So... f'(x) is positive for all real x (do you see why?), this means the function is always increasing... therefore it cannot cross the x axis more than once.

agentredlum is offline  
April 16th, 2013, 01:40 AM   #3
Joined: Apr 2012

Posts: 21
Thanks: 0

Re: Intermediate Value Theorem

Oh my. I just had the biggest facepalm moment.

Thank you so much, you just saved me a sleepless night
hooperoo is offline  

  My Math Forum > College Math Forum > Real Analysis

intermediate, theorem

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Intermediate value theorem nubshat Calculus 1 October 23rd, 2013 01:32 AM
intermediate value theorem chris123 Real Analysis 0 February 21st, 2013 06:44 PM
continuous and intermediate value theorem frankpupu Real Analysis 1 February 7th, 2012 11:16 PM
continuous and intermediate value theorem frankpupu Calculus 4 January 31st, 2012 02:56 AM
Help with the Intermediate Value Theorem Twoxsmart Calculus 1 January 28th, 2009 10:55 PM

Copyright © 2019 My Math Forum. All rights reserved.