Facebook Page
Twitter
RSS
+ Reply to Thread
Results 1 to 2 of 2
  1. MHB Journeyman
    MHB Math Helper
    Fernando Revilla's Avatar
    Status
    Offline
    Join Date
    Jan 2012
    Location
    Madrid, Spain
    Posts
    661
    Thanks
    1,720 time
    Thanked
    1,707 time
    Thank/Post
    2.582
    #1
    Here is the question:

    Quote Quote:
    Show that the function f(x)=(x-a)^2*(x-b)^2+x takes on the value (a+b)/2 for some value of x.?
    Here is a link to the question:



    I have posted a link there to this topic so the OP can find my response.

  2. # ADS
    Circuit advertisement
    Join Date
    Always
    Location
    Advertising world
    Posts
    Many
     

  3. MHB Journeyman
    MHB Math Helper
    Fernando Revilla's Avatar
    Status
    Offline
    Join Date
    Jan 2012
    Location
    Madrid, Spain
    Posts
    661
    Thanks
    1,720 time
    Thanked
    1,707 time
    Thank/Post
    2.582
    #2 Thread Author
    Hello Karla,

    The function $f(x)=(x-a)^2(x-b)^2+x$ is continuos in $\mathbb{R}$ (polynomical function). Besides, $f(a)=a$ and $f(b)=b$.

    But $\dfrac{a+b}{2}$ is the middle point of the segment with endpoints $a$ and $b$ (no matter if $a<b$, $b<a$ or $a=b$) so, $\dfrac{a+b}{2}$ is included between $a$ and $b$. According to the Intermediate Value Theorem, there exists $x\in\mathbb{R}$ such that $f(x)=\dfrac{a+b}{2}$.

Similar Threads

  1. lamps's question at Yahoo! Answers about the Intermediate Value Theorem
    By Fernando Revilla in forum Questions from Other Sites
    Replies: 1
    Last Post: January 30th, 2013, 05:13
  2. Ken's Question from Yahoo Answers: Probability Question For Verification?
    By CaptainBlack in forum Questions from Other Sites
    Replies: 0
    Last Post: October 14th, 2012, 01:37
  3. dbiebs question from Yahoo Answers
    By Yahoo Answers in forum Questions from Other Sites
    Replies: 1
    Last Post: August 26th, 2012, 12:53
  4. Posterior distribution question Pixie's question from Yahoo Answers
    By CaptainBlack in forum Advanced Probability and Statistics
    Replies: 1
    Last Post: April 28th, 2012, 03:51
  5. David's question from Yahoo Answers
    By CaptainBlack in forum Advanced Probability and Statistics
    Replies: 1
    Last Post: April 9th, 2012, 02:21

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Math Help Boards