Question

Find the critical points of the function
f(x,y)=x^3-6xy+3y^2-24x+4
Also classify them in Relative Maxima, Relative Minima and Saddle Points.

Answer 1

First find the first partial derivatives (fx) and the first partial derivative (fy).
fx= 3x^2-6y-24=0
fy=-6x+6y=0
From these two equations you find the two critical points which are (-2,-2) and (4,4)
After that you use the second derivative test (D=fxxfyy-(fxy)^2)
In the case of (-2,-2) D<0 and so it is a saddle point.
In the case (4,4) D>0 and fxx<0 and so it is a minimum point

Answer 2

Thank you very much...