Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Trending News

Promoted
Jeremy
Lv 5
Jeremy asked in Science & MathematicsMathematics · 6 years ago

Minimize distance between two quadratics.?

Find the shortest distance between

f(x) = x² + 1

and

f(x) = √x

(approximated within 5 decimal places)

Attachment image

2 Answers

Relevance
  • cidyah
    Lv 7
    6 years ago

    Let y = x^2+1 - sqrt(x)

    y' = 2x - 1/ (2 sqrt(x) )

    y' = 2x - 1 / (2 sqrt(x)) = 0

    2x = 1/ (2sqrt(x))

    x sqrt(x) = 1/4

    x^(3/2) = 1/4

    [x^(3/2)]^(2/3) = (1/4)^(2/3)

    x = (1/4)^(2/3)

    x= 0.39685

    y' = 2x - (1/2) x^(-1/2)

    y'' = 2 -(1/2)(-1/2) x^(-3/2)

    y'' = 2 + 1 /(4 x^(3/2)) > 0 when x= (1/4)^(2/3) ; so y has been minimized

  • ?
    Lv 7
    6 years ago

    h(x) = x^2 + 1 - sqrt(x)

    h ' (x) = 0 = 2x - 1/2 x^(-1/2)

    2x = 1/2 x^(-1/2)

    x^5/2 = 1/4

    x = (1/4)^(2/5) = answer

Still have questions? Get your answers by asking now.