violetagamez2

violetagamez2

24.06.2019 •

Mathematics

Consider the function represented by the equation 6q equals 3x -9 right there equation in function notation work you is the independent variable

Solved

Show answers

Ответ:

juliannabartra

12.02.2023

f(x,y)=9+xy-x-2y

$\implies\begin{cases}f_x=y-1=0\implies y=1\\f_y=x-2=0\implies x=2\end{cases}$

which tells you that the only critical point of f(x,y)

f(x,y)

occurs at (2, 1), which does lie within the region

. At this point, we get f(2,1)=7

f(2,1)=7

.

Next we check along the boundaries of

. They are the lines x=1

x=1

with $0\le y\le4$ , y=0

y=0

with $1\le x\le5$ , and y=5-x

y=5-x

with $1\le x\le5$ .

If x=1

x=1

, then

f(1,y)=8-y

, which is monotonically decreasing and must therefore attain its maximum at y=0

y=0

and minimum at y=4

y=4

. We get

f(1,0)=8

and

f(1,4)=4

.

If

y=0

, then

f(x,0)=9-x

, which is also monotonically decreasing and attains its maximum at x=1

x=1

and minimum at x=5

x=5

. We get

f(1,0)=8

and

f(5,0)=4

.

If

y=5-x

, then

f(x,5-x)=g(x)=-x^2+6x-1

. We have $g'(x)=-2x+6=0\implies x=3$ , which suggests an extremum occurs at (3, 2). We get f(3,2)=8

f(3,2)=8

.

So

f(x,y)

has a minimum value of 4 at (1, 4) and (5, 0), and a maximum value of 8 at (1, 0) and (3, 2).

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice