MuPAD Pro Computing Essentials - Examples 

Example 12.7 - Finding Extremes of Function of two Variables

This is another typical example. We have a function of two variables and we wish to produce its local extremes. 

f := (x,y)->(x^2 - y^2)*exp(-x^2 - y^2); //declare function
 
EQ1 := diff(f(x,y), x); //produce df/dx
 
EQ2 := diff(f(x,y), y); //produce df/dy
 

EQ1 := expand(EQ1*exp(x^2 + y^2))=0; //simplify EQ1
EQ2 := expand(EQ2*exp(x^2 + y^2))=0; //simplify EQ2
  

solve({EQ1,EQ2}, {x,y}); //solve equations

{[x = 0, y = 0], [x = 0, y = -1], [x = 0, y = 1], 
[x = -1, y = 0], [x = 1, y = 0]}

f(0,0), f(0,-1), f(0,1), f(-1,0), f(1,0); // produce values

0, -exp(-1), -exp(-1), exp(-1), exp(-1)
 

float(-exp(-1)), float(exp(-1)); 

-0.3678794412, 0.3678794412