Results 1 to 5 of 5

Math Help - Finding equation given inflection point

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    119

    Finding equation given inflection point

    \displaystyle f(x)=\sqrt{x+1}+\frac{b}{x}

    Find \displaystyle b such that \displaystyle f(x) has a point of inflection at \displaystyle x=3

    Answer in the back has it at \displaystyle \frac{27}{64}, but I'm not sure how to do it.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901
    For a point of inflection, \displaystyle\frac{d^2y}{dx^2}=0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2010
    Posts
    119
    Quote Originally Posted by Quacky View Post
    For a point of inflection, \displaystyle\frac{d^2y}{dx^2}=0
    Meaning I'd have to solve \displaystyle f''(3)=0 right? That's what I tried, but I got a completely different answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901
    Let me have a go.

    f(x)=\displaystyle (x+1)^{\frac{1}{2}}+\frac{b}{x}
    <br />
f'(x)=\displaystyle\frac{1}{2}(x+1)^{-\frac{1}{2}}-\frac{b}{x^2}

    f''(x)=\displaystyle -\frac{1}{4}(x+1)^{\frac{-3}{2}}+\frac{2b}{x^3}

    When x=3, f''(x)=0

    I carried on from here, and was able to get the correct answer of \frac{27}{64}, but I admit that I initially made a differentiation error myself.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2010
    Posts
    119
    Quote Originally Posted by Quacky View Post
    Let me have a go.

    f(x)=\displaystyle (x+1)^{\frac{1}{2}}+\frac{b}{x}
    <br />
f'(x)=\displaystyle\frac{1}{2}(x+1)^{-\frac{1}{2}}-\frac{b}{x^2}

    f''(x)=\displaystyle -\frac{1}{4}(x+1)^{\frac{-3}{2}}+\frac{2b}{x^3}

    When x=3, f''(x)=0

    I carried on from here, and was able to get the correct answer of \frac{27}{64}, but I admit that I initially made a differentiation error myself.
    Thanks a lot! These kind of questions really annoy me>.< Thanks again
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the Point of Inflection
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 1st 2010, 07:26 PM
  2. Replies: 0
    Last Post: November 3rd 2009, 10:18 AM
  3. Finding max mins point of inflection.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 4th 2009, 05:50 PM
  4. Finding minima/maxima/point of inflection
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 1st 2009, 07:52 PM
  5. Replies: 1
    Last Post: February 2nd 2009, 02:09 PM

Search Tags


/mathhelpforum @mathhelpforum