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
denis-greek [22]
3 years ago
7

Find the minimum and maximum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f

(x, y) = x2y + x + y, xy = 5
Mathematics
1 answer:
nata0808 [166]3 years ago
8 0
Via Lagrange multipliers:

L(x,y,\lambd)=x^2y+x+y+\lambda(xy-5)
L_x=2xy+1+\lambda y=0
L_y=x^2+1+\lambda x=0
L_\lambda=xy-5=0

\underbrace{10}_{2xy}+1+\lambda y=0\implies \lambda=-\dfrac{11}y
xy=5\implies y=\dfrac5x\implies\lambda=-\dfrac{11}5x

\impliesx^2+1+\left(-\dfrac{11}5x\right)x=0\implies x^2=\dfrac56\implies x=\pm\sqrt{\dfrac56}
xy=5\implies y=\pm\sqrt{30}

At these points, we get local minima of f\left(\pm\sqrt{\dfrac56},\pm\sqrt{30}\right)=\pm2\sqrt{30}.

- - -

Another way to do this is to make f(x,y) a function independent of y, which is made possible by the constraint.

xy=5\implies y=\dfrac5x
\implies f(x,y)=f\left(x,\dfrac5x\right)=F(x)=6x+\dfrac5x
\implies F'(x)=6-\dfrac5{x^2}=0\implies x=\pm\sqrt{\dfrac56}

and so on.
You might be interested in
Pete is solving for x in the problem to the right. He has decided that these angles are supplementary as 4x+16 is also the measu
Liula [17]
The answer is 764 yards your
welcome
3 0
3 years ago
Please helpp <br> 25 = (a - 29/10
dedylja [7]

Step-by-step explanation:

If you like my answer than please mark me brainliest and follow me thanks

3 0
3 years ago
Determine the intercepts of the line.<br> x-intercept: (___,___)<br> y-intercept: (___,___)
valentina_108 [34]

Answer:

x-intercept: (-40,0)

y-intercept: (0,15)

Step-by-step explanation:

5 0
3 years ago
How do you convert set notation to interval notation?
Semenov [28]

Answer:

Imagine we are to express  [ a , b ]  in set notation

A = [ a , b ] , then  A = { x  ∈  R  /  a ≤ x ≤ b }

In this notation we define the characteristics of all  x  belonging to this set  A ....x must be greater or equal to a and simultaneously smaller or equal to b...

Interval notation is other way to say the same but assuming that  means the extreme a is IN the interval and  means extreme  a  is not.

6 0
3 years ago
B) Write 6.04 * 10 as an ordinary number.
Eddi Din [679]

Answer:

60.4

Step-by-step explanation:

6.04*10=60.4

i hope ti helps you

3 0
3 years ago
Other questions:
  • Can someone explain how to do this
    10·2 answers
  • Molly can read four-fifths of a page in the time it takes kayla to read one page. how many pages will kayla read in the time it
    8·1 answer
  • Group of 7 people spend 33.50 movie tickets 6.50 adults and 3.50 for child ticket. Which system of equation could be used to fin
    8·2 answers
  • (3/2)x - -4 =13 what is x?
    10·1 answer
  • A card is selected at random from a standard deck. find each probability. randomly selecting a club or a 3
    10·1 answer
  • 14+6÷2=20÷2=10 yes or no
    14·2 answers
  • . Isabella buys a 1.75 litre carton of apple juice. What is the largest number of 200 millilitre glasses that she can have from
    6·1 answer
  • 2. A jeweler bought an antique watch for $500. He then sold it in his store $850. What was the percent of change in the price of
    5·1 answer
  • Hiiiiiii hiiiiiiiii ji​
    12·2 answers
  • Find the distance between each pair of points
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!