Question

Given the function f (x, y) = ax^2

2 + 2xy + ay.y

2-ax-ay. Take

for a an integer value that is either greater than 1 or less
than -1, and

then determine the critical point of this function. Then
indicate whether it is

is a local maximum, a local minimum or a saddle point.

Given the function f (x, y) = ax^2 +2 + 2xy + ay^2-2-ax-ay.
Take

for a an integer value that is either greater than 1 or less
than -1, and

then determine the critical point of this function. Then
indicate whether it is

is a local maximum, a local minimum or a saddle point.

Answer #1

Examine the function f(x, y) = 2x 2 + 2xy + y 2 + 2x − 3 for
relative extrema.
Use the Second Partials Test to determine whether there is a
relative maximum, relative minimum, a saddle point, or insufficient
information to determine the nature of the function f(x, y) at the
critical point (x0, y0), such that fxx(x0, y0) = −3, fyy(x0, y0) =
−8, fxy(x0, y0) = 2.

Find the location of the critical point of the function
f(x,y)= kx^(2)+3y^(2)-2xy-24y (in terms of k) of
t. The classify the values of k for which the critical
point is a:
I) Saddle Point
II) Local Minimum
III) Local Maximum

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).

Problem 1.
(1 point)
Find the critical point of the function
f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)).
c=?
Use the Second Derivative Test to determine whether it is
A. a local minimum
B. a local maximum
C. test fails
D. a saddle point

1. Calculate the total diﬀerential for the given function.
G(x,y) = e^5x ·ln(xy + 1)
2. Apply the Second Derivative Test to the given function and
determine as many local maximum, local minimum, and saddle points
as the test will allow.
F(x,y) = y^4 −7y^2 + 16 + x^2 + 2xy

Consider the function f(x,y) = -8x^2-8y^2+x+y
Select all that apply:
1. The function has two critical points
2. The function has a saddle point
3. The function has a local maximum
4. The function has a local minimum
5. The function has one critical point
*Please show your work so I can follow along*

a) The function f(x)=ax^2+8x+b, where a and b are
constants, has a local maximum at the point (2,15). Find the values
of a and b.
b) if b is a positive constand and x> 0, find the
critical points of the function g(x)= x-b ln x, and determine if
this critical point is a local maximum using the second derivative
test.

Determine the absolute minimum and maximum values of the
function f(x, y) = 2x^2 −2xy +y^2 −2y + 7 on the closed triangular
region with vertices (0, 0), (3, 0), and (0, 3).

Let f(x,y) = 3x^2 + cos(Pi*y). a) f has a saddle point at (0,k)
whenever k is an odd integer b) f has a saddle point at (0,k)
whenever k is an even integer) c) f has a local maximum at (0,k)
whenever k is an even integer d) f has a local minimum at (0,k)
whenever k is an odd integer.

f (x, y) =(x ^ 4)-8(x ^ 2) + 3(y ^ 2) - 6y
Find the local maximum, local minimum and saddle points of the
function.
Calculate the values of the function at these points

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