Results 1 to 3 of 3

Thread: maximum value of func.

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    17

    maximum value of func.

    $\displaystyle f(x)=2(a-x)(\sqrt{x^2+b^2} + x) $

    for all real x,
    show the maximum value of f(x) is $\displaystyle ( a^2+b^2)$
    and $\displaystyle x=\frac{a^2-b^2}{2a}$ when f(x) is maximum
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi stud_02!

    Quote Originally Posted by stud_02 View Post
    $\displaystyle f(x)=2(a-x)(\sqrt{x^2+b^2} + x) $

    for all real x,
    show the maximum value of f(x) is $\displaystyle ( a^2+b^2)$
    and $\displaystyle x=\frac{a^2-b^2}{2a}$ when f(x) is maximum
    For all real x? Your Solution seems to be wrong,
    if a=0 it does not make any sense

    And by the way, if b = 1 and a = 0
    $\displaystyle f(x) = -2x(\sqrt{x^2+1}+x)$ has its maximum in $\displaystyle \approx (-0.34 ; -1.66)$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jan 2009
    Posts
    715
    Quote Originally Posted by stud_02 View Post
    $\displaystyle f(x)=2(a-x)(\sqrt{x^2+b^2} + x) $

    for all real x,
    show the maximum value of f(x) is $\displaystyle ( a^2+b^2)$
    and $\displaystyle x=\frac{a^2-b^2}{2a}$ when f(x) is maximum
    Substitute
    $\displaystyle t = \sqrt{x^2+b^2} + x$
    $\displaystyle \implies$
    $\displaystyle t^2 - 2tx + x^2 = x^2 + b^2 $
    $\displaystyle \implies$

    $\displaystyle x = \frac{t^2-b^2}{2t}$

    Go back to the function ,

    we will have
    $\displaystyle f(t) = -t^2 + 2at + b^2 $

    $\displaystyle = -(t-a)^2 + b^2 + a^2 $

    so it has max. value $\displaystyle a^2 + b^2 $ when $\displaystyle t = a$
    $\displaystyle x = \frac{a^2-b^2}{2a}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Application - exp. func.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Apr 17th 2011, 09:13 PM
  2. Application - exp. func.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Apr 17th 2011, 07:53 PM
  3. exp func
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Aug 24th 2009, 06:43 PM
  4. Need help!! logarithms and exp.func thx!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 24th 2009, 10:13 AM
  5. Fam. of func.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 27th 2008, 04:56 PM

Search Tags


/mathhelpforum @mathhelpforum