Suppose f(x,y)=(x-y)(16-xy). Answer the following 1. Find the local maxima of

percibaa8

percibaa8

Answered question

2021-12-20

Suppose f(x,y)=(xy)(16xy). Answer the following
1. Find the local maxima of f.
2. Find the local minima of f.
3. Find the saddle points of f.

Answer & Explanation

lalilulelo2k3eq

lalilulelo2k3eq

Beginner2021-12-21Added 38 answers

f(x,y)=(xy)(16xy)
fx=(16xy)+(xy)(y)=16xy+y2xy
fy=(xy16)+(xy)(x)=xy16x2+xy
fx=0  y22xy16=0; y2=x2
fy=0  x22xy16=0; y=±x
y=x  x22x2+16=0  x2=16  x=±4
y=x  x2+2x2+16=0  x2=163 - not possible
(x,y)=(4,4),(4,4)
f×=2y; fyy=2x; fxy=2x+2y
D=4xy4(xy)2
D(4,4)=4(16)=64<0
D(4,4)=4(16)=64<0
psor32

psor32

Beginner2021-12-22Added 33 answers

Concretise the answer, please
nick1337

nick1337

Expert2021-12-28Added 777 answers

1) none 2) none 3) (-4,-4,0), (4,4,0)

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