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Optimization - Finding Minimum Between (0,0) and e^x

  1. Dec 29, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the minimum distance from the origin to the curve y = e^x.


    2. Relevant equations

    Distance Formula

    3. The attempt at a solution

    [​IMG]

    5-6 bright Calculus kids in my high school grappled with this problem and we couldn't find an answer.

    Can anyone verify my solution? To simplify calculations, I minimized the inner quantity (underneath the square root of the Distance Formula). I feel, though, that this may have changed the answer. Answers are so close that I may have made a mistake.
     
  2. jcsd
  3. Dec 29, 2008 #2

    tiny-tim

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    Hi carlodelmundo! :smile:
    Looks good to me. :biggrin:

    (and minimising the inner quantity x2 + e2x is the same as minimising √(x2 + e2x)) :smile:
     
  4. Dec 29, 2008 #3
    okay! just checking. Thank you tiny-tim.

    I thought that since the derivatives of √(x^2 + e^2x)) and x^2 + e^2x are different, there could have been a discrepancy in my answer.
     
  5. Dec 29, 2008 #4

    tiny-tim

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    nah … if f'(x)/2√(f(x)) = 0, then that's the same as f'(x) = 0 (unless f(x) can be infinite). :wink:
     
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