no message from Minimize[] on a weird function(x^x) !?!

*To*: mathgroup at smc.vnet.net*Subject*: [mg96724] no message from Minimize[] on a weird function(x^x) !?!*From*: congruentialuminaire at yahoo.com*Date*: Sun, 22 Feb 2009 03:12:39 -0500 (EST)

Hello MathGroup: I have: f[x_]=x^x Plot[f[x],{x,-3,3.}] What makes this a weird function is that when x<0, the function is discontinuous and non-differentiable and has a global minimum at -1. To answer the question: "what is the minimum of this function", I tried FindMinimum[f[x],{x,2}] (* this appears correct *) > {0.692201, {x -> 0.367879}} FindMinimum[f[x],{x,2}] (* this complains about the gradient, but appears correct *) > FindMinimum::nrgnum: The gradient is not a vector of real numbers at {x} = {-1.}. >> > {-1., {x -> -1.}} NMinimize[f[x], x] (* this gives the minimum in the positive domain *) > {0.692201, {x -> 0.367879}} Minimize[f[x], x] (* this gives no answer and no error message *) > Minimize[x^x, x] Is this expected behavior? TIA. Roger Williams Franklin Laboratory