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Maximum of a function u(x,t)

  1. Oct 10, 2004 #1
    I have u(x,t)=-2xt-x^2 find maximum in region {-2 ≤ x ≤ 2 , 0 ≤ t ≤ 1}

    I believe to find the critical point first I have to take the partial derivative with respect to x and t and equate to zero.
    Ux=-2t-2x = 0
    Ut=-2x = 0

    Thus the only critcal point I find is x=0, t=0.
    But the maximum (answer at back of book) is x=-1, t=1 => u(-1,1)=1

    Where did I go wrong?
  2. jcsd
  3. Oct 10, 2004 #2


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    That's because (0, 0) is a saddle point (check the second derivatives!). You need to examine the absolute maximum of the function in the region.
  4. Oct 10, 2004 #3
    Ok, got it. I forgot that then I need to evaluate along the boundaries of the region.
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