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5 calculus problems that needs answers. They are all shown on the photos that I attached. Thank you.

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Question 9

4 pts

Find the maximum value of f(x, y) = 2xy on the ellipse 3×2 + y2 = 3.

9

1

1

3

0 3

13

1

-1

V3

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lij

IC

مجله

25

2

9

E

2

K

M

Question 11

4 pts

Consider the function f(x, y) = x3 – tan(2y) at the point P (1, 0). Which of the

following is/are true?

P. The maximum rate of change of fat P is 10.

Q. f does not change at P in the direction (-3,2).

R. There exists a unit vector û such that Dù f(P) = 2.

OP and R

O P and Q

OR only

O Q and R

O Q only

A

Question 12

4 pts

дz

If z = (x + y)2, where x = ln(2s – t) and y = 2st, find

Әt

s=1

t=1

8

O 16

0 4

O 12

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Question 13

6 pts

Let f(x,y)

1

x2y +3. Find the following:

3

=

1. How many critical points does f have?

(enter a, b, c, d, or e)

a. infinitely many

b. 1

c. 2 d. 3

e. O

2. Find the extreme values of f on the region D.

x² + y² = 27

D

absolute maximum =

A

absolute minimum =

(enter integers or fractions; enter none if no such value exists)

Question 14

6 pts

A contour map for f(x, y) is given below. Determine the sign of the partial derivative at

the points P and Q.

у

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UF

FLORIDA

6 pts

Question 14

A contour map for f(x, y) is given below. Determine the sign of the partial derivative at

the points P and Q.

G @ 3個

y у

DOO

DOR

349

Z

?

X

-2

1

-1 +

W

1.

af

(P)

[ Select]

0

მყ

2.

af

(Q)

дх

[ Select]

0

Question 15

6 pts

Let f(x, y) = (3×2 – 2y2.

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Tags:

Surveying in mathematics

mathematics knowledge

surveying mathematics

Mathematical elements

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