Question

f(x,y)= x^2-y^2+xy-10x+3
a.) critical point
b.) maximun, minimum or saddle point

Answer 1

fx= 2x+y-10 fxx= 2 fxy=1
fy=-2y+x fyy=-2
fy= -2y+x=0 ---> x=2y
fx= 2x+y-10 --> 2(2y)+y-10=0
---> 4y+y=10 ---> y=2
x=2y--> x= 2*2= 4
the point is (2,2)
then search D
D= fxx*fyy-(fxy)^2
= -4 -1 = -5, D<0, means saddle

Answer 2

fx= 2x+y-10 fxx= 2 fxy=1
fy=-2y+x fyy=-2
fy= -2y+x=0 ---> x=2y
fx= 2x+y-10 --> 2(2y)+y-10=0
---> 4y+y=10 ---> y=2
x=2y--> x= 2*2= 4
the point is (2,2)
then search D
D= fxx*fyy-(fxy)^2
= -4 -1 = -5, D<0, means saddle

Answer 3

u can find the other point