Question

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

Answer #1

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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

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...

1)Find an equation of the tangent plane to the surface given by
the equation xy + e^2xz +3yz = −5, at the point, (0, −1, 2)
2)Find the local maximum and minimum values and saddle points
for the following function: f(x, y) = x − y+ 1 xy .
3)Use Lagrange multipliers to find the maximum and minimum
values of the function, f(x, y) = x^2 − y^2 subject to, x^2 + y 4 =
16.

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).

1. At x = 1, the function g( x ) = 5x ln(x) −
3x
is . . .
Group of answer choices
has a critical point and is concave up
decreasing and concave up
decreasing and concave down
increasing and concave up
increasing and concave down
2. The maximum value of the function f ( x ) = 5xe^−2x
over the domain [ 0 , 2 ] is y = …
Group of answer choices
10/e
0
5/2e
e^2/5...

f(x)=x^3-4x^2+5x-2
Find all critical numbers of the function, then use the second
derivative test on each critical number to determine if it is a
local maximum or minimum. Show your work.

You are given that the function f(x,y)=8x2+y2+2x2y+3 has first
partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second
partials fxx(x,y)=16+4y, fxy(x,y)=4x and fyy(x,y)=2. Consider the
point (0,0). Which one of the following statements is true?
A. (0,0) is not a critical point of f(x,y).
B. f(x,y) has a saddle point at (0,0).
C. f(x,y) has a local maximum at (0,0).
D. f(x,y) has a local minimum at (0,0).
E. The second derivative test provides no information about the
behaviour of f(x,y) at...

For the function f(x, y)=ln(1+xy)
a.Find the value of the directional derivative of f at the point
(-1, -2) in the direction <3,4>.
b.Find the unit vector that gives the direction of steepest
increase of f at the point (2,3).

Given the function g(x)=4x^3−24x^2+36x, find the first
derivative, g'(x)
g′(x)= ???
Notice that g'(x)=0 when x=1, that is, g'(1)=0
Now, we want to know whether there is a local minimum or local
maximum at x=1, so we will use the second derivative test.
Find the second derivative, g''(x)
g''(x)=????
Evaluate g"(1)
g''(1)=???
Based on the sign of this number, does this mean the graph of g(x)
is concave up or concave down at x=1?
[Answer either up or down --...

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

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