If a polynomial has two local maxima and two local minima, can it be of odd degree?

Answers

Answer 1

Answer:

  yes, it can be of odd degree

Step-by-step explanation:

The local maxima and minima correspond to zeros in the derivative of the function. The degree of the polynomial will be 1 more than some multiple of 2 greater than the number of zeros in the derivative.

__

based on derivative

For 2 each of local maxima and minima, the derivative will have 2+2 = 4 real zeros. The degree of the polynomial will be 1 greater, hence of degree 5 (or more). The polynomial must be of odd degree.

__

based on behavior away from extrema

The local extrema must alternate: a maximum must be followed by a minimum, or vice versa. When there are an even number of each kind, the end extrema will be of opposite kinds. The end behavior of the function will be upward from a minimum and downward from a maximum. Hence the end behaviors must be in opposite directions--characteristic of an odd-degree polynomial.

The polynomial must be of odd degree.

_____

Additional comment

A polynomial with real coefficients will have an even number of complex roots. The complex roots of the derivative of a polynomial have no effect on the number or kind of extrema.

__

Attached is an example of a polynomial with 2 maxima and 2 minima. It is of 5th degree.

If A Polynomial Has Two Local Maxima And Two Local Minima, Can It Be Of Odd Degree?

Related Questions

Calculate the area of a triangle with a base of 6 cm and a height of 12 cm

Answers

Answer:

36

Step-by-step explanation:

12 x 6 = 72 / 2 = 36 because the area of a triangle is base times height divided by 2

Answer: 36 cm^2

Step-by-Step Explanation:

Base (b) = 6 cm
Height (h) = 12 cm

Area = 1/2 * b * h

Therefore,
= 1/2 * b * h
= 1/2 * 6 * 12
= 1 * 3 * 12
= 3 * 12
= 36

Area = 36 cm^2

A(n) ___ function is the function that sometimes results when the independent variable of a function is exchanged with the dependent variable.

Answers

The A(n) is inverse function is the function that sometimes results when the independent variable of a function is exchanged with the dependent variable.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We know that the inverse of a function, sometimes known as an anti function, is a function that can be reversed into another.

In other words, if a function "f" converts x to y, the inverse of the same function will convert y to x. The inverse function is denoted by f⁻¹ or F⁻¹ if the function is denoted by 'f' or 'F'.

Thus, the A(n) is inverse function is the function that sometimes results when the independent variable of a function is exchanged with the dependent variable.

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round your final answer to the nearest degree ​

Answers

Answer:

The correct answer is 37°

5 yrs ago, Nuri was thrice as old as Sonu. 10 yrs later, Nuri will be twice as old Sonu. How old are Nuri n Sonu?​

Answers

Answer:

Answer will be 50

Step-by-step explanation:

Let us suppose, present age of Nuri be ‘x’ years and present age of Sonu be ‘y’ years.

Now, it is given that five years ago, Nuri was thrice old as Sonu. Hence,

Five years ago,

Nuri’s age = x-5 years

Sonu’s age = y-5 years

And relation between ages can be given as

Nuri’s age = 3×sonu’s age or

x-5 = 3(y-5)

x-5 = 3y-15

x-3y+10 = 0 ………..(i)

Another relation is given in the problem that ten years later, Nuri is twice as old as Sonu.

So, ten years ago,

Nuri’s Age = x+10

Sonu’s Age = y+10

And relation between ages can be written as

x+10 = 2(y+10)

x+10 = 2y+20

x-2y-10 = 0 …………..(ii)

Now we can solve the equation (i) and (ii) to get values of x and ‘y’ or present ages of Nuri and Sonu.

Value of ‘x’ from equation (i) be

x = 3y-10 ……….(iii)

Putting value of ‘x’ from equation (iii) in equation (ii) we get,

3y-10-2y-10 = 0

y = 20

Now, from equation (iii) value of ’x’ can be given as,

x= 3(20)-10

x = 50

Hence, the present ages of Nuri and Sonu are 50 years and 20 years respectively.

A survey indicated that 4 out of 6 doctors used brand X aspirin. If 3600 doctors were surveyed, how many used brand X?

Answers

Answer: 2,400 doctors used brand X aspirin.

Step-by-step explanation: The question notifies us that 3,600 total doctors were surveyed. This automatically lets us know that 6/6 doctors = 3,600 doctors. We can find the unit rate from this point by dividing 3,600 by 6. We will find that 600 doctors represents 1/6 doctors. We can multiply our unit rate by 4 to find that 4 out of 6 doctors, or 2,400 doctors, use brand X aspirin. 4/6 of 3,600 is 2,400, so 2,400 doctors used brand X aspirin. Hope this helps!

Answer:

1200 doctors

Step-by-step explanation:

60% of doctors use brand X aspirin.

So, what is 60% of 2000?

(0.6) (2000) = 1200

1200 out of the 2000 use brand X.

At a cake stall , muffins cost $2 each & cookies cost $1 each. The cake stall earned $146. If 2 more cookies than muffins were sold, how many muffins were sold?

Answers

Answer:

48 muffins were sold

Step-by-step explanation:

Represent the number of muffins by m and the number of cookies by c.

Then the revenue from the sales of muffins was ($2/muffin)m and that from the sales of cookies ($1/cookie)c.  Remembering that c = m + 2, we obtain the following equation:

($2/muffin)m +  ($1/cookie)(m + 2) = $146, so that:

2m + 1m + 2 = 146, or 3m + 2 = 146, or 3m = 144.

Dividing both sides of this result by 3, we get m = 48

Thus, 48 muffins were sold.

If the scale factor is three and the center of origin is (1,1) dilate the coordinates A(-5,-7) B(-6,-5) C(-2,-3)

Answers

here’s the answer! hope it helps

Finding the relationship of two lines

Answers

[tex]Explanation[/tex]

This is very basic all you have to look at is the 2x because whenever the number has a variable with [tex]x[/tex] it means its the slope and the slope will tell you whether they are parallel or perpendicular.

so as you can see the slopes are alike because they are both 2x

Thus, the answer is Parallel

//-carry on learning-//

1. Solve the quadratic function by graphing. x²-3x - 18 - 0​

Answers

Answer:

that's easy all you have to do is find out what is the value of x then divided by 2 once you divide by 2 subtract 3x 18 and 0

How should this model be completed to represent 1,881 ÷ 33?

Answers

Answer:

Check the attached image below

a bicycle wheel has a diameter of 65cm what is the length of one revolution of the wheel PLEASE HELP​

Answers

AnswerAnswerAnswerAnswer: C = πd = 65π = 204.2 cm

Step-by-step explanation: C = pi*d

where d is the diameter.

First we get the circumference, then we multiply it by the number of revolutions, which is 20:

C = 3.14 * 65

C = 204.1 cm (this is only equal to 1 revolution)

Therefore, total distance travelled in after 20 revolutions is

204.1 * 20 = 4082 cm

204.2 is the answer to the question

13. Figure QRSP is a rectangle.
Q.
100°
What is the measure of angle RPS?
A. 40 degrees
C. 80 degrees
B. 50 degrees]

Answers

Answer:

b 50 degrees bavaggagshdd

ASAP!!!
Alicia found $1.90 on the beach. Her brother found three times as much money. How much money did Alicia and her brother find in total?
Please be accurate!

Answers

Answer: The correct answer is $7.60.

Step-by-step explanation: First, you multiply 1.90 and 3. This gives you 5.7. Then, you add 1.9. This gives you $7.60.

Answer:

£7.60

Step-by-step explanation:

Alicia found £1.90, we can give this the value x

Her brother found triple the amount, or 3x

In total they found 4x

If £1.90 is x, 4x is £7.60

I need the answer for this question please

Answers

The sum of √30 + √50 lies between 12 and 13.

What is the sum of the numbers?

The square root of a number can be described as number that when multiplied with itself yields that number.

√30 = 5.48

√50 = 7.07

5.48 + 7.07 = 12.55

The consecutive integers are 12 and 13

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ZA=C
Round your answer to the nearest hundredth.
C
B
6
8
A
?

Answers

Answer:

? = 41.41°

Step-by-step explanation:

The known side length is adjacent to the angle we need to find hence we will use cosine

cosx = adjacent /hypotenuse

cos(?) = 6 / 8

simplify fraction, cos(?) = 3 / 4

? = arccos(3 / 4)

Is anyone able to solve this equation? It’s urgent

Answers

Answer:

1500

Step-by-step explanation:

You can find the complete solution in the given attachment

What is the probability of rolling a two on the first die and a three on the second die?

Answers

Answer:

a dice has 1 two and 1 three

1/6 *1/6 =1/36

Solve the quadratic equations by completing the square.
x^2-4x=-1

Answers

Answer:

2 ± √3

Step-by-step explanation:

Solving quadratic equation by completing squares:  

           x² - 4x = -1

Divide the coefficient of x by 2.

                 4 ÷ 2 = 2

 Now, square the result and add that to both sides of the equation.

          2² = 2* 2 = 4

          x² - 4x + 4 = -1 + 4

          x² - 4x + 4 = 3

         x² - 2 * x * 2 + 2² = 3

    Compare it with a² - 2ab + b² . Now , a = x and b = 2

            (x - 2)² = 3

    Take square root both sides

             x - 2 = ±√3

                    x = 2 ± √3

Solutions: x = 2 +√3   ;  2 - √3

What is k equal to if StartFraction 7.6 over 2 EndFraction = StartFraction 9.5 over k EndFraction?
1.6
2.5
3.8
4.8

Answers

2.5 is the answer! trust to this! :) 2.5

Is 12/19 rational or irrational?

Answers

Answer:

irrational

Step-by-step explanation:

Convert (728), to base 10​

Answers

Answer:

2D8

Step-by-step explanation:

To convert decimal number 728 to hexadecimal, follow these steps:

step 1 =Divide 728 by 16 keeping notice of the quotient and the remainder.

step 2 =Continue dividing the quotient by 16 until you get a quotient of zero.

step 3 =Then just write out the remainders in the reverse order to get hexadecimal equivalent of decimal number 728.

Using the above steps, here is the work involved in the solution for converting 728 to hexadecimal number:

728 / 16 = 45 with remainder 8

45 / 16 = 2 with remainder 13 (D)

2 / 16 = 0 with remainder 2

Then just write down the remainders in the reverse order to get the answer, The decimal number 728 converted to hexadecimal is therefore equal to :

2D8

A school wants 2 chaperones for every 25 students on a field trip. There are 100 students going on the field trip. How many chaperones does the school need?
A
4

B
8

C
108

D
50

Answers

Using proportions, it is found that the number of chaperones that the school needs is given by:

B. 8.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 2 chaperones are needed for every 25 students. How many are needed for 100 students? The rule of three is given by:

2 chaperones - 25 students

n chaperones - 100 students

Applying cross multiplication:

25n = 2 x 100

n = 200/25

n = 8.

Hence option B is correct.

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Determine whether the successive probabilities are independent or dependent events.

15) The probability of getting 4 tails in a row when flipping a coin?
a) Independent
b) Dependent

16) The probability of drawing 2 Queens in a row from a deck of cards?
a) Independent
b) Dependent ​

Answers

Answer:

15)  a) independent 16)  b) Dependent ​

Step-by-step explanation:

15) let T1 be the event : “get a tail in the first flip”

    let T2 be the event : “get a tail in the second flip”

p(T1 ∩ T2) = 1/4

p(T1) = 1/2

p(T2) = 1/2

Then

p(T1) × p(T2) = (1/2)(1/2 = 1/4

Since ,p(T1 ∩ T2) = 1/4 = p(T1) × p(T2)

Then the events are independent.

16) These events are dependent since we don’t  replace the Queen before the second draw.

The two Events are dependent because the probability that we draw a Queen  in the first draw affect the probability that we draw a Queen in the second draw.

Find the area of a regular polygon with 7 sides that has a side length of 6 inches and an apothem of 8 inches.

Area = [?]in2

Answers

Answer:

see the attachment photo!

Need one person help for math Plato class

Answers

Answer:

The answer is B. 13.7 inches

i hope this can help you! :)

alex has a box of 250 nails. he uses 80 nails. then he loses 35 nails. how many nails does alex have left? what is the hidden question

Answers

The answer is 100+30+5

In algebra, there are lots of rules and properties to remember. The good news is that once you understand them, you can apply them in lots of different orders and combinations. Give an example of a mathematic problem that can be solved in multiple ways by applying properties of algebra differently. Explain your reasoning.

Answers

Algebraic properties can be applied in any mathematical equation.

How to explain the algebraic property?

There are several algebraic properties; they include:

Distributive propertyAdditive propertyInverse propertyCommutative propertyAnd so on

All these properties can be applied in a mathematical equation.

An instance is as follows:

3(x + 2) = 18

Method 1

Apply the distributive property

3x + 6 = 18

Apply the subtraction property of equality

3x = 12

Apply the division property of equality

x = 4

Method 2

Apply the division property of equality

x + 2 = 6

Apply the subtraction property of equality

x = 4

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G.MG.3 Beth is going to enclose a rectangular area in back of her house. The house wall will form one of the four sides of the fenced in area, so Beth will only need to construct three sides of fencing. Beth has 48 feet of fencing. She wants to enclose the maximum possible area.

Answers

The maximum area of the rectangular path is when the length is 24 feet and the width is 12 feet.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width. Hence:

There is 48 feet of fencing:

x + 2y = 48

x  = 48 - 2y   (1)

The area (A) is:

A = xy = y(48 - 2y)

A = 48y - 2y²

The maximum area is at A' = 0, hence:

48 - 4y = 0

y = 12

x = 48 - 2(12) = 24

The maximum area of the rectangular path is when the length is 24 feet and the width is 12 feet.

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Solve for x to the nearest tenth.
Can someone help me?​ Multi-Step Diagrams

Answers

Answer:

Step-by-step explanation:

Math work class rell

Answers

Answer:

The answer is D. infinite.

Answer:

infinte

Step-by-step explanation:

→ For any value of x which is substituted you will get that value

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