1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Max/Min Problems

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data
    A rectangle is bounded by the X-axis and the semicircle Y = [(sqrt)36-x^2]. What dimensions should the rectangle have so that its area is a maximum.

    2. Relevant equations

    Just a note, the 36-x^2 is all under the radical.

    3. The attempt at a solution

  2. jcsd
  3. Oct 30, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    Well, the width of the rectangle is clearly [itex]2x[/itex], and its height is [itex]y=\sqrt{36-x^2}[/itex]....so what is its area [itex]A(x)=?[/itex] for a given value of [itex]x[/itex]? How do you find the maximum of such a function?

    P.S. I don't think the definition of "ditto" is exactly what you seem to think it is (just a friendly FYI)
  4. Oct 30, 2008 #3
    Wouldn't I just find the area by multiplying both of them together?
  5. Oct 30, 2008 #4


    User Avatar
    Homework Helper
    Gold Member

    Sounds good to me; the last time I checked the area of a rectangle was just width times height ;0)
  6. Oct 30, 2008 #5
    So I multiply them together then take the derivative, and then find the critical points of that?
  7. Oct 30, 2008 #6


    User Avatar
    Science Advisor

    Yes, now do it!
  8. Oct 30, 2008 #7

    Many thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook