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*

Find the critical point of the function f(x,y)=x2+y2+xy+12x
c=________
Use the Second Derivative Test to determine whether the point
is
A. a local maximum
B. a local minimum
C. a saddle point
D. test fails

If f(x,y)=(5∗x3+4∗y3+4∗x∗y+1) find the critical point for
f(x,y)
x=____
y=____
Is this critical point a local maximum, local minimum, or saddle
point?

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).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 15 minutes ago

asked 17 minutes ago

asked 22 minutes ago

asked 26 minutes ago

asked 32 minutes ago

asked 38 minutes ago

asked 47 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago