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
snow_lady [41]
3 years ago
15

How does the domain change when finding the extremum of a function with and without constraints

Mathematics
1 answer:
Lisa [10]3 years ago
3 0

Answer:

if we want to find the maximum or minimum of a function, there are some methods, like see where the derivate is equal to zero and such.

Now, if we have a constraint, for example x> 4

This obviously changes the domain of the possible points where we can find the extremum.

But particularly, we can check at x  = 4 and see it there is a maximum.

if the constraint is x > 4, then then we may found a upper/lower bound.

if the constraint is x ≥ 4, then we may find a maximum/minimum.

Now, when we work with more complex situations, like find the maximum value of f(x) while we have the constraint g(x) = x^4 + x^3 + x^2 = 5

Then the domain will be equal to the intersection of the domains of both functions:

This means, the only possible values that we can input in f(x) to search the extremes, are the values of x such that x^4 + x^3 + x^2 = 5, so this relation defines our new domain (remember that f(x) also may have problems in some values of x, this is why we take the intersection of the domains of f(x) and g(x))

This means that constraints can limit a lot the domain of our functions.

You might be interested in
Use the appropriate property of determinants to find<br> a.a. do not evaluate the determinants.
yan [13]
Bunininonucyvunijojko
3 0
2 years ago
David will spend at most $39 on gifts. So far, he has spent $22. What are the possible additional amounts he will spend? Use c f
iren2701 [21]

Answer:

c\leq \$17

Step-by-step explanation:

Let

c -----> the additional amount (in dollars) David will spend

we know that

The word " at most" in this context means "less than or equal to"

The amount David has spent plus possible additional amounts he will spend must be less than or equal to $39

so

The inequality that represent this situation is

22+c\leq 39

solve for c

subtract 22 both sides

c\leq 39-22

c\leq \$17

The maximum amount he could spend is $17

7 0
3 years ago
The length of a rectangle is 7 more than the width. The area is 744 sqaure yards, find the length and width of the rectangle​
AVprozaik [17]

Answer:

  • Length of rectangle is 31 yards and Width is 24 yards.

Given:

  • The length of a rectangle is 7 more than the width.
  • The area is 744 sqaure yards

Solution:

Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.

Using formula

\\  \:  \:  \:  \:  \pink{ \dashrightarrow \:  \:  \:  \:  \sf { \underbrace{Area_{(Rectangle)} =  Length × Width  }}} \\  \\

On Substituting the required values, we get;

\\ \: \: \: \:  \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \:  \dashrightarrow \: \: \: \: \sf  {x}^{2}  + 7x = 744 \\ \\ \\ \: \: \: \:  \dashrightarrow \: \: \: \: \sf  {x}^{2}  + 7x - 744 = 0 \\ \\ \\  \: \: \: \:  \dashrightarrow \: \: \: \: \sf  {x}^{2}  + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \:  \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \:  \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \:  \dashrightarrow \: \: \: \: \sf x = 24 \:  or \:   - 31 \\ \\

As we know that width of the rectangle can't be negative. So x = 24

<u>Hence</u>,

  • Width of rectangle = x = 24 yards
  • Length of the rectangle = x + 7 = 31 yards

\thereforeLength of rectangle is 31 yards<u> </u>and Width is 24 yards.

8 0
2 years ago
MZAOB = 6x- 12°<br> mZBOC = 3x+ 30°<br> Find mZAOB:
Elanso [62]
The answer is 14 hope is right
4 0
2 years ago
Read 2 more answers
Is .277277277 irrational
prisoha [69]
Nope. Your problem is not irrational
4 0
3 years ago
Other questions:
  • What is the answer to this : Expand y(y + 10)
    10·1 answer
  • Which side lengths form a right triangle?
    15·1 answer
  • Mrs morales wrote a test with 15 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocab
    6·1 answer
  • PLZ help dividing exponents 7^12 ÷ 7^4 is equal to _____. 1^3 3 7^3 7^8
    6·2 answers
  • Sharon is 42 years old. Her daughter is 12 years old. How many years ago was Sharon 4 times older than her daughter?
    15·2 answers
  • Need a little bit of help
    15·1 answer
  • What value of g makes the equation true? (x+7)(x-4)=x²+gx-28
    7·1 answer
  • Help quick it due! Please hurry lol
    14·1 answer
  • Your friend deposits $1900 in an account that earns 6% compounded
    10·2 answers
  • 16 more than craigs score is 62
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!