Question

Find and classify the critical plints of the given function
f(x,y) =xy^2+yx^2-x

Answer #1

Find the Critical point(s) of the function f(x, y) = x^2 + y^2 +
xy - 3x - 5. Then determine whether each critical point is a local
maximum, local minimum, or saddle point. Then find the value of the
function at the extreme(s).

consider the 2 variable function f(x,y) = 4 - x^2 - y^2 - 2x -
2y + xy
a.) find the x,y location of all critical points of f(x,y)
b.) classify each of the critical points found in part a.)

2. Consider the function f(x, y) = x 2 + cos(πy). (a) Find all
the Critical Points of f and (b) Classify them as local
maximum/minimum or neither

Is the function f(x,y)=x−yx+y continuous at the point (−1,−1)?
If not, why is the function not continuous?
Select the correct answer below:
A. Yes
B. No, because lim(x,y)→(−1,1)x−yx+y=−1 and f(0,0)=0.
C. No, because lim(x,y)→(−1,1)x−yx+y does not exist and f(0,0)
does not exist.
D. No, because lim(x,y)→(0,0)x2−y2x2+y2=1 and f(0,0)=0.

Let f (x, y) = (x −
9) ln(xy).
(a)
Find the the critical point (a, b). Enter the
values of a and b (in that order) into the answer
box below, separated with a comma.
(b)
Classify the critical point.
(A) Inconclusive (B) Relative Maximum (C) Relative Minimum (D)
Saddle Point

Introduction to differential equations
1. y' = x-1+xy-y
2. x^2 y' - yx^2 = y

z= f(x,y) = xy-2x-3y+6 has one critical point (x,y,z). Please
find it
2) f(xx)=
3) f(xy)=

Use Lagrange multipliers to find the maximum value of the
function f(x,y) = xy given the constraint x+y=10

Find the absolute maximum and minimum values of the function f
(x, y) = x^2 xy+on the region R bounded by the graphs of y = x^2
and y = x+ 2

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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