1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mama L [17]
2 years ago
7

Find the local maximum and minimum values and saddle point(s) of the function.

Mathematics
1 answer:
iogann1982 [59]2 years ago
4 0
f(x,y)=9e^y(y^2-x^2)
\nabla f=\left\langle-18xe^y,9ye^y(2+y)\right\rangle

Critical points occur where the gradient is zero. This is guaranteed whenever x=0 and either y=0 or y=-2.

The Hessian matrix for this function looks like

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-18e^y&-18xe^y\\-18xe^y&9e^y(2-x^2+4y+y^2)\end{bmatrix}

and has determinant

|H(x,y)|=-162e^{2y}(2+x^2+4y+y^2)

Maxima occur whenever the determinant is positive and f_{xx}. Minima occur whenever both the determinant and f_{xx} are positive. Saddle points occur whenever the determinant is negative.

At (0,0), you have a saddle point since the determinant reduces to -324, so (0,0,0) is the saddle point.

At (0,-2), the determinant is \dfrac{324}{e^4}>0 and f_{xx}(0,-2)=-\dfrac{18}{e^2}, so \left(0,-2,\dfrac{36}{e^2}\right) is a local maximum.

No other critical points remain, so you're done.
You might be interested in
Which one is the correct answer
galben [10]
Jim can do the 1/2 of floor in 4 hours
pete completes 1/2 of floor in 2 hour

therefor, since, pete took 1/2 as much time, pete can tile 2 times as many tiles (logic)

pete can lay 25 more than jim
if pete is 2 times of jim
p=2j
and pete is 25 more than jim
p=25+j
2j=p=25+j
2j=25+j
minus j
j=25

jim lays at 25 tiles per hour
C is answer
6 0
3 years ago
The graph represents f(x), and g(x) = 7x – 42.
Aliun [14]
g(x)=7x-42\\\\\y-intercept\ of\ g(x):\\\\f(0)=7\cdot0-42=-42\to(0;\ -42)\\\\x-intercept\ of\ g(x):\\\\0=7x-42\ \ \ \ |+42\\7x=42\ \ \ |:7\\x=6\to(6;\ 0)

f(x)=ax+b\\\\y-intercept\ of\ f(x):\ (0;\ -3)\\\\x-intercept\ of\ f(x):\ (6;\ 0)

Answer:

A) the y-intercept of g(x) is less than the y-intercept of f(x).


4 0
3 years ago
Please help! Correct answer only, please! I need to finish this assignment this week. Given matrix A and B both have dimensions
Delicious77 [7]

Answer:

Option B is correct

Step-by-step explanation:

The multiply of matrix A by matrix B that is inverse of A, must result in an identity matrix that has form shown in option B

Hope this helps!

8 0
3 years ago
The population of a city has increased by 36% since it was last measured. If the current population is 51000 , what was the prev
PilotLPTM [1.2K]

So if we have the number after the 36% increase in population, we would want to subtract that 36% from 51000.

36% of 51000 can be found by multiplying 51000 by 0.36 (0.36 is the decimal equivalent of 36%)

51000 x .36 = 18360

So you simply subtract 18360 from 51000, which is 32,640.

6 0
3 years ago
Calculate the future value of $7,000 earning 6% interest compounded quarterly for 7 years. (Round your answer to two decimal pla
qwelly [4]

Use the compound interest formula.

Let A = the ending amount

Let P = the principal

Let r = the interest rate

Let n = the amount compounded a year

Let t = time

A = P(1 + r/n) ^(n/t)

Substitute your numbers in

A = $7,000(1 + 0.06/4)^(4/7)

Solve for A

A = $7,059.81

7 0
3 years ago
Other questions:
  • What does x equal in this equation?
    12·2 answers
  • A sample of 300 guests at Universal Orlando theme parks in 2015 were selected and each was asked whether they were staying at on
    10·1 answer
  • A rectangular-prism-shaped toy chest is 2 \text { m}2 m2, start text, space, m, end text by 1 \text { m}1 m1, start text, space,
    13·1 answer
  • Maya was asked to find 70% of 400. what steps should she complete to find the missing part
    7·1 answer
  • How do I round decimals?
    13·2 answers
  • Need help !!! Cant figure this question out
    5·1 answer
  • WILL GIVE A BRAINLIEST!!
    14·2 answers
  • Suppose you have 3 bags. Two of them contain a single $10 bill, and the third contains a single $5 bill. Suppose you pick one of
    14·1 answer
  • A coordinate grid is shown below. 12 11 -1 0 -1 -2 Part A: Which point represents the origin? (2 points) Part B: Starting from t
    7·1 answer
  • The circumference of an ellipse is approximated by…
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!