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
patriot [66]
3 years ago
14

Find all the points at which the direction of fastest change of the function f(x, y) = x2 + y2 − 4x − 2y is i + j.

Mathematics
1 answer:
Luda [366]3 years ago
7 0

Answer:

All the points that lie on the line:

y(x)=x-1

Step-by-step explanation:

In order to find the maximum rate of change, we need to find the gradient of the function. The gradient of a function of two variables is defined to be:

\nabla f =\frac{\partial f}{\partial x} i + \frac{\partial f}{\partial y} j

So:

\frac{\partial f}{\partial x} = 2x-4=2(x-2)\\\\\frac{\partial f}{\partial y} = 2y-2=2(y-1)

Hence:

\nabla f(x,y)=2(x-2)i+2(y-1)j

Since we need to find all the points at which the direction of fastest change of the function f(x,y)=x^{2} +y^{2} -4x-2 is i+j. Then:

2(x-2)i+2(y-1)=ai+aj\\\\a>0

Therefore:

2(x-2)=2(y-1)\\\\Solving\hspace{3}for\hspace{3}y\\\\y=x-1

So, we can conclude, that all the points where the direction of fastest change of f(x,y) lie on the line:

y(x)=x-1

You might be interested in
Fill in the table using this function rule.<br> y = 5x+4
olya-2409 [2.1K]
No idea man

Explanation: I don’t man I just wang pints
3 0
3 years ago
What is the graph of y = 2f(x)
Licemer1 [7]

HERE IS YOUR ANSWER...

I THINK THIS MAY SOLVE YOUR DOUBT....

THANK YOU......

8 0
3 years ago
20% of a spring basket is peeps. There are 8 peeps. What is the total number of items in the basket?
murzikaleks [220]
8*100=20*x
800  =20x
40    =x 
40 items are in the basket 
5 0
3 years ago
Read 2 more answers
*order of operation<br> 296-(65•2-32/4
gulaghasi [49]

Answer:

174

Step-by-step explanation:

start with the numbers inside the parenthesis! next, multiply (65 x 2) = 130, then divide (32/4) = 8. then, subtract 130-8 to get 127. now move outside the parenthesis and subtract 296-127 = 174!

7 0
2 years ago
What does 3x2 + 9x − 30
Harlamova29_29 [7]

Answer:38

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Algebra2 <br>|2-3(2w+1)=7w-3(7+w)
    14·1 answer
  • Martha is putting a wallpaper border along the top of four walls in her bedroom. The room is rectangle that measures 12 ft. by 1
    7·1 answer
  • Which transformation was performed on triangle ABC to produce triangle A’ B’ C’
    13·1 answer
  • The answer <br> The answer
    13·2 answers
  • What is 41 divided by 17 as a decimal rounded to the nearest tenth.
    14·1 answer
  • Please answer ASAP<br><br><br>y=5/8b+10 for b, ill give brainliest and show work plz
    11·1 answer
  • -9/5x+3/5y=2 <br> please need the answer asap
    11·1 answer
  • Howard needs to buy pens and pencils for work. Pens cost $0.40 each and pencils cost 50.25 each. He needs to buy at least 340
    15·1 answer
  • Can someone tell me what this is <br><br><br> 6% OF 56% X 60% X 40%
    6·2 answers
  • Z(0,-5) Go left 5, up right, and down 3.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!