222 - Topic 10 - Work for standard extrema

3204 days ago by Professor222

var('x,y') # f(x,y) = x^3+y^3-6*x^2+9*y^2+12*x+27*y+19 # f(x,y) = (x-1)^2*(y+4)^2 f(x,y) = x^3*y+x+y^2 fx = diff(f,x) fy = diff(f,y) fxx = diff(fx,x) fxy = diff(fx,y) fyy = diff(fy,y) 
       
solns = solve([fx,fy],(x,y),solution_dict=true) for soln in solns: show(soln) 
        

                                
                            

                            
                                

                                    

                                

                            
                                

                                    
                                

                        

                    		
                

            

        

        


    




  
    

    
    






    


        
        
        
            
                
            
            
                
for soln in solns:
   (soln[x],soln[y]) 

            
            

            

        

        
        
        

            

                

                    
                               
                    
                    
                        

                            

                                
                                    

                                
                            

                            
                                

                                    

                                

                            
                                

                                    
                                

                        

                    		
                

            

        

        


    




  
    

    
    






    


        
        
        
            
                
            
            
                
x0 = solns[4][x]
y0 = solns[4][y]
G = plot3d(f,(x,x0-1,x0+1),(y,y0-1,y0+1))
G += point3d((x0,y0,f(x=x0,y=y0)),color='red',size=30)
show(G)