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Gradient of functions with multiple variables

  1. Oct 19, 2007 #1
    1. The problem statement, all variables and given/known data
    The gradient of f(x,y) = x^2-x+y is:

    gradient_f(x,y) = (2x-1 ; 1). To find gradient_f(x,y), I set 2x-1 = 0 and 1 = 0 - so there are no points, where gradient_f(x,y) is zero because of 1 != 0?
     
  2. jcsd
  3. Oct 19, 2007 #2
    And how to I find the maximum and minimum of the function, when there are no stationary points? (gradient_f(x,y) != 0)
     
  4. Oct 19, 2007 #3
    It's been awhile since I did Calc 3, but if you're in a bounded domain, you can apply the Extreme Value Theorem. Under those circumstances, the max/min likely lie on the boundary.
     
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