Question

Find the relative extreme values of the function.

f(x, y) = 3xy − 2x^{2} − 2y^{2} + 14x − 7y −
2

Answer #1

Find the relative extreme values of the function. (If an answer
does not exist, enter DNE.)
f(x, y) = 3xy − 2x2 − 2y2 + 42x − 21y −
6
relative maximum
relative minimum

Find all local extreme values of the function
f(x,y)=2x2−3y2−4xy−4x−16y+1.

Determine the global extreme values of the function
f(x,y)=2x3+2x2y+2y2,x,y≥0,x+y≤1
fmin=
fmax=

Find the relative extreme values of the function. (If an answer
does not exist, enter DNE.)
f(x, y) =
−x3 − y2
+ 768x − 32y
relative max:
relative min:

Find the exact extreme values of the function z = f(x, y) = x^2
+ (y-19)^2 + 70 subject to the following constraints x^2 + y^2
<= 225 Complete the following: Fmin=____at(x,y) (__,__)
Fmax=____at(x,y) (__,__)

Let f(x,y)=3xy−5x2−2y2
Then an equation for the tangent plane to the graph of ff at the
point (3,3)(3,3) is

Find the exact extreme values of the function z = f(x, y) =
(x-3)^2 + (y-3)^2 + 43
subject to the following constraints: 0 <= x <= 17
0 <= y <= 12
Complete the following: Fmin=____at(x,y) (__,__)
Fmax=____at(x,y) (__,__)

Find the linearization of the function
f(x,y)=40−4x2−2y2−−−−−−−−−−−−√f(x,y)=40−4x2−2y2 at the point (1,
4).
L(x,y)=L(x,y)=
Use the linear approximation to estimate the value of
f(0.9,4.1)f(0.9,4.1) =

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 ) =

f(x,y)=xy ; 4x^2+y^2=8
Use Lagrange multipliers to find the extreme values of the
function subject to the given constraint.

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