Question

Find the local maximum and minimum values and saddle point(s) of the function f ( x , y ) = f(x,y)=xe^(-2x2-2y2). If there are no local maxima or minima or saddle points, enter "DNE."

The local maxima are at ( x , y ) = (x,y)= .

The local minima are at ( x , y ) = (x,y)= .

The saddle points are at ( x , y ) =

Answer #1

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f (x, y) =
xy − 5x − 5y
− x2 −
y2
local
maximum value(s)
local
minimum value(s)
DNE
saddle
point(s)
(x, y,
f)
=DNE

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) =
4y
cos(x), 0 ≤
x ≤ 2π
Find:
local maximum value(s) =
local minimum value(s) =
saddle point(s) (x,y,f) =

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = xy + 8/x+8/y
local maximum value(s)
local minimum value(s)
saddle point(s)
(x, y, f)
=

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = xy + 64/x+64/y
local maximum value(s)
local minimum value(s)
saddle point(s)
(x, y, f)
=

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) =
y2 − 4y
cos(x), −1 ≤
x ≤ 7
local
maximum value(s)
local
minimum value(s)
saddle
point(s)
(x, y,
f)
=

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.) f(x,
y) = 4y cos(x), 0 ≤ x ≤ 2π local maximum value(s) local minimum
value(s) saddle point(s) (x, y, f) =

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) =
y2 − 4y cos
x, −1 ≤
x ≤ 7
local
maximum value(s)
local
minimum value(s)
saddle
point(s)
(x, y,
f)
=

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter
DNE.)
f(x, y) = 2x3 − 6x + 6xy2
local maximum value(s)
local minimum value(s)
saddle point(s)
(x, y, f) =

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) =
x3 − 48xy +
64y3
local
maximum value(s)
local
minimum value(s)
saddle
point(s)
(x, y,
f)
=

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) =
6ey(y2
− x2)
local
maximum value(s)
local
minimum value(s)
saddle
point(s)
(x, y,
f)
=

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