Find the critical points and classify them as local maxima, local minima, saddle points, or none of
Submitted : 20180614 06:05:39 Popularity:
Tags: points classify Find critical minima
f(x,y) = (x^2)y + (2y^2)  6xy + 1
f(x,y) = (x^2)y + (2y^2)  6xy + 1
∂f/∂x = f_x = 2xy6y = 2y(x3) = 0
∂f/∂y = f_y = x^26x+4y = 0
Points are
(0,0), (3,9/4) and (6,0)
∂^2f/∂x^2 = f_xx = 2y
∂^2f/∂y^2 = f_yy = 4
f_xy = 2x6
H = f_xx*f_yy  (f_xy)^2
At (0,0)
H = 036 = 36 (Saddle Point)
At (6,0)
H = 036 = 36 (Saddle Point)
At (3, 9/4)
H = (9/2)*4  9 = 9 (Minimum)
Per WolframAlpha:
Definition:
A point of a function's graph where the 1st derivative is either zero or undefined.
f_x = 2 xy  6y = 2 y ( x  6) ; f_y = x² + 4 y 6 x..> f_y = 0 means 4y = 6 x  x²> f_x = 0 means either y = 0 or x = 6...
points ( 0 , 0 ) , ( 6 , 0 ) ; ...f_xx = 2y ; f_yy = 4 ; f_xy = 2x  6...both are saddles
First, can you sate here whats the procedure to find/classify the critical points?
State it here and we can then take it from there,,,


Article Source:
www.Aphotolog.Com
Answer Questions