Homework SourseFind and classify the critical points of each function fxy
Find and classify the critical points of each function
f(x,y) = 2x^3+xy^2+5x^2+y^2
Answer:
local max of 125/27 @ (-5/3,0)
local min of 0 at (0,0)
saddle pts at (-1,2) (-1,-2)
f(x,y) = 2x^3+xy^2+5x^2+y^2
Answer:
local max of 125/27 @ (-5/3,0)
local min of 0 at (0,0)
saddle pts at (-1,2) (-1,-2)
Solution
6x*X + y*y + 10x = 0 2xy + 2y = 0 => y=0 and x = -1 y=0 , x=0 , -5/3 x=-1 , y = +/ - 2 second derivative : 12x + 10 : x = 0 minima x = -1 maxima x = -5/3 , maxima second derivative wrt y : 2x + 2 hence choosing x, y pair : local max (-5/3 , 0) : y=125/27 local min : (0,0) : y = 0 saddle points : (-1,2) : y=3 and (-1,-2) : y = 3
