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Local min/max/saddle points of 3d graphs

  1. Jun 22, 2010 #1
    Hello, just got done taking a test and one problem kinda confused me.

    1. The problem statement, all variables and given/known data

    f(x,y) = e^x cos y

    find local min/max and saddle points

    2. Relevant equations

    fx = e^x cos y
    fy = -e^x sin y

    3. The attempt at a solution

    I answered that there were no critical points for this function and therefore no extrema. I looked at a graph of this here. To me, those sharp crevices indicate the function is not differentiable at those points. Is this correct?
  2. jcsd
  3. Jun 22, 2010 #2


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    Science Advisor

    No. [itex]e^x cos(x)[/itex] and [itex]e^x sin(x)[/itex] (and, in fact, are infinitely differentiable) for all x and y. Those peaks look like "sharp crevices" only because your scale is too large.
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