Results 1 to 6 of 6

Math Help - Proof there is a root

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    64
    Thanks
    4

    Proof there is a root

    Proof there is at least one root:
    e^x = 3 - 2x

    can you just do 0 = 3 - 2x
    x = 1.5 ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by Daniiel View Post

    can you just do 0 = 3 - 2x
    x = 1.5 ?
    No you can't, you could graph both e^x and 3 - 2x

    If they intersect you have proven there is a solution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    64
    Thanks
    4
    Thanks

    Do you think thats all they want?
    Not like a written out proof and a value for the intercept?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87
    Quote Originally Posted by Daniiel View Post
    Thanks

    Do you think thats all they want?
    Not like a written out proof and a value for the intercept?
    If they don't specify what method to use, you should be able to use graphing. You should definitely do this unless you're doing a introductory calculus course. If you are doing an intro calculus course, they may want you to consider the following:

    You can prove a solution exists without graphing, but you won't be able to find the exact value of the solution.

    I won't go into detail here because the graphing should suffice. Basically note that e^x is always increasing (look at the derivative to see why) and 3 -2x is always decreasing. Since they both exist for all real x, and the range for y = 3 - 2x is all real values of y, they must intersect at some point. To write it out proper you may have to look into the intermediate value theorem.
    Last edited by Gusbob; April 26th 2010 at 06:29 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,646
    Thanks
    1596
    Awards
    1
    Quote Originally Posted by Daniiel View Post
    Proof there is at least one root:
    e^x = 3 - 2x
    Let f(x)=e^x+2x-3
    Then f(0)=-2<0~\&~f(1)-e+2-3>0.
    Therefore there is a root between 0 & 1.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Sep 2008
    Posts
    64
    Thanks
    4
    Thanks
    i'll do both
    i didn't think they're give us another IV thrm question because we got one in the last assignment and i thought you might have to prove its continuous aswell
    Thanks again
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another Trigonometry Root Proof
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: June 11th 2011, 08:24 AM
  2. N-th Root Irrationality Proof
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: May 5th 2011, 09:25 PM
  3. proof that if a square is even then the root is too.
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: February 3rd 2011, 11:55 AM
  4. [SOLVED] Proof: Primative root mod(p)
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: August 10th 2010, 05:52 PM
  5. Primitive Root proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 25th 2010, 11:32 AM

Search Tags


/mathhelpforum @mathhelpforum