Homework SourseIdentify and determine the nature of the critical points of
Identify and determine the nature of the critical points of the given function.
f(x, y, z) = x^2 + y^2 + 2z^2 + xz
f(x, y, z) = x^2 + y^2 + 2z^2 + xz
Solution
partial diff wrt x : 2x + z = 0 second partial diff wrt x : 2 hence it is minima partial diff wrt y : 2y = 0 second partial dif : 2 hence it is minima partial diff wrt z : 4z + x = 0 second partial diff : 4 hence it is minima solving x+4z =0 and 2x + z = 0 global minima (0,0,0) , it has maxima at (infinity, infintiy ,infinity)
