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: 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

    HallsofIvy

    User Avatar
    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook