Determine the location and values of the absolute maximum and absolute minimum of given function: f(x)= ( -x+2)^4, Where 0<=x<=3

Answers

Answer 1

Answer:

The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

Step-by-step explanation:

First, we obtain the first and second derivatives of the function by chain rule and derivative for a power function, that is:

First derivative

[tex]f'(x) = -4\cdot (-x+2)^{3}[/tex]

Second derivative

[tex]f''(x) = 12\cdot (-x + 2)^{2}[/tex]

Then, we proceed to do the First and Second Derivative Tests:

First Derivative Test

[tex]-4\cdot (-x+2)^{3} = 0[/tex]

[tex]-x + 2 = 0[/tex]

[tex]x = 2[/tex]

Second Derivative Test

[tex]f''(2) = 12\cdot (-2+2)^{2}[/tex]

[tex]f''(2) = 0[/tex]

The Second Derivative Test is unable to determine the nature of the critical values.

Then, we plot the function with the help of a graphing tool. The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

Determine The Location And Values Of The Absolute Maximum And Absolute Minimum Of Given Function: F(x)=

Related Questions

Kevin correctly answered 75% of 32 test questions.

Part A
How many questions did Kevin answer correctly?



Part B
How many more questions would Kevin have to answer correctly to get more than 80% correct?

Answers

Answer:

part a-24 questions

part b-2 or 3 more questions

Step-by-step explanation:

part a-to find the number, change the percent into a decimal (.75) and multiply (24)

part b-first find how many questions need to be right to get 80% (.80 times 32=25.6). then subtract by how many he would get with a 75% (25.6-24=about 2 to 3 more questions, rounded 2)

The rule g = b + 3 expresses the relationship between the
number of girls g and the number of boys b in a classroom.
Rewrite this rule another way.

Answers

Answer:

g = 3 + b

b + 3 = g

3 + b = g

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

Rewriting the rule so 'b' would be the subject:

[tex]g = b + 3\\\\g - 3 = b + 3-3\\\\g-3=b\\\\\boxed{b=g-3}[/tex]

Hope this helps.

Joe bought a cylindrical water tank for his garden, but he forgot to ask the seller what the diameter of the tank was. He needs to know the diameter of the tank so that he can build a platform for it to sit on. The seller told him the Volume and the height, calculate the diameter of the tank using the information below. The volume of the tank is 300π 〖ft〗^3 and its height is 10ft.

Answers

Answer:

1.7ft

Step-by-step explanation:

Given data

Volume of tank=  300π 〖ft〗^3

Height of tank= 10ft

The expression for the volume of a cylinder is given as

Volume= πr^2h

Substitute

300π = π *r^2*10

300= r^2*100

3= r^2

r= √3

r= 1.7 ft

Hence the radius of the cylinder is 1.7ft

Don’t need to send the math or anything just need the answer will give brainliest!!!

Answers

Answer:

920

Hope that this helps!

Can someone work please so I can understand how

Answers

Answer:

[tex]\text{A. }\frac{4\sqrt{14}}{{7}}[/tex]

Step-by-step explanation:

In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Therefore, we can form a right triangle with non-right angle [tex]\theta[/tex] and its opposite side [tex]\sqrt{7}[/tex] and its adjacent side [tex]5[/tex].

By definition, [tex]\csc \theta=\frac{1}{\sin\theta}[/tex].

In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle. To find the hypotenuse, use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.

Solving, we get:

[tex]5^2+\sqrt{7}^2=c^2,\\25+7=c^2,\\c^2=32,\\c=\sqrt{32}=4\sqrt{2}[/tex]

Therefore, we have:

[tex]\csc \theta = \frac{1}{\sin \theta}=\frac{1}{\frac{\sqrt{7}}{4\sqrt{2}}},\\\\\csc \theta=1\cdot \frac{4\sqrt{2}}{\sqrt{7}},\\\\\csc \theta =\frac{4\sqrt{2}}{\sqrt{7}}\cdot \frac{\sqrt{7}}{\sqrt{7}}=\boxed{\text{A. }\frac{4\sqrt{14}}{{7}}}[/tex]

Answer: Choice A)   [tex]\frac{4\sqrt{14}}{7}[/tex]

======================================================

Explanation:

Refer to the figure below. We start off drawing a right triangle that has opposite side sqrt(7) and adjacent side 5.

This is because tan = opposite/adjacent.

Use the pythagorean theorem to find the hypotenuse is sqrt(32) which simplifies like so

sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)

The last thing to do is to take the ratio of the hypotenuse over the opposite side. Recall that csc, aka cosecant, is the reciprocal of sine.

sin = opposite/hypotenuse

csc = hypotenuse/opposite

---------

So we get the following

[tex]\csc{\theta} = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc{\theta} = \frac{4\sqrt{2}}{\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2*7}}{\sqrt{7*7}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{\sqrt{49}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{7}\\\\[/tex]

So that's why the answer is choice A.

I need help with this question
v2–2v–24

Answers

Answer:

(v - 6)(v + 4)

Step-by-step explanation:

v² - 2v - 24

v² + 4v - 6v - 24

v(v + 4) - 6(v + 4)

(v - 6)(v + 4)

Hey guy, can yall please help me?

Answers

Answer:

x is greater than or equal to 3

Step-by-step explanation:

x ≥ 3

x is greater than or equal to 3

so you got the plot right

María compra mercancía por valor $2.000.000 la cual tiene una utilidad estimada del 25%, ella desea saber el valor que ganara al vender toda su mercancía ¿Cuál sera el valor que corresponde a las ganancias de maría?

Answers

Answer:

Maria buys merchandise worth $ 2,000,000 which has an estimated profit of 25%, she wants to know the value that she will earn by selling all her merchandise. What will be the value that corresponds to Maria's earnings?

Step-by-step explanation:

2,500,000 $ worth of merchandise

Please help I’ll give brainliest

Answers

Answer:

v = 27,000 mm³

Step-by-step explanation:

v = s³

v = 30³

v = 27,000 mm³

It’s the third option

Use long division to find the quotient below.
(8x) + 20x2 + 36) divide (2x+6)
A. 4x2 - 6x+6
B. 8x2 - 8x+6
C. 4x2 - 2x+6
D. 8x2 - 4x + 6

Answers

Given:

[tex]8x^3+20x^2+36[/tex] divided by [tex](2x+6)[/tex].

To find:

The quotient by using long division method.

Solution:

We have,

Dividend = [tex]8x^3+20x^2+36[/tex]

Divisor = [tex](2x+6)[/tex]

Using long division method we get

[tex]\underline{2x+6}|\overline{8x^3+20x^2+0x+36}|\underline{4x^2-2x+6}[/tex]

          [tex]\underline{8x^3+24x^2}[/tex]

                   [tex]-4x^2+0x[/tex]                                 (After subtraction)

                  [tex]\underline{-4x^2-12x}[/tex]

                             [tex]12x+36[/tex]                          (After subtraction)

                             [tex]\underline{12x+36}[/tex]

                                [tex]\underline{\quad 0\quad }[/tex]                           (After subtraction)

The quotient is [tex]4x^2-2x+6[/tex].

Therefore, the correct option is C.

Six teammates are competing for first, second, and third place in a race.

How many possibilities are there for the top three positions?

20
30
120
240

Answers

Step-by-step explanation:

there Are 120 possibilities for the top three positions

We will see that there are 120 different possibilities for the top 3 positions.

How many possibilities are there for the top three positions?

Here we need to count the number of options for each of the positions.

For the first position, there are 6 options (6 team members).For the second position, there are 5 options (because one is already in the first position).For the third position, there are 4 options.

The total number of different combinations is given by the product between the numbers of options, we will get:

C = 6*5*4 = 120

There are 120 different possibilities for the 3 positions.

If you want to learn more about combinations, you can read:

https://brainly.com/question/11732255

#SPJ2

Juice is sold in two different sizes. An 18 gl oz bottle costs $1.10. A 36 gl oz bottle costs 2.75. Which is better to buy?

Answers

Answer:

The 18 ounce bottle costs less per ounce and is the better buy

Step-by-step explanation:

First find the cost per ounce for the 18 ounce bottle

1.10 / 18 =.0611111 per ounce

Then find the cost per ounce for the 38 ounce bottle

2.75 / 36 =.076388888

The 18 ounce bottle costs less per ounce

I need some help; if you don't know the answer, don't answer

Answers

Answer:

B is the right answer and if you want learn this, than learn algebric expression

B is the answer for the question

1. Jennifer bought 4 1/2 pounds of hamburger for $22.50.
What was the cost per pound?

Answers

Answer:

.20$

Step-by-step explanation:

4 1/2=4.5

4.5 divided by 22.50=.20

Answer: Jennifer bought 4 1/2 pounds of hamburger for $22.50.

What was the cost per pound?

.20cents

Question 4 of 10 Based only on the information given in the diagram, it is guaranteed that A ABC - AXYZ. 3 Y Z O A. True B. False​

Answers

Answer: True

Step-by-step explanation:

We know in every triangle all the angles add up to 180 so for triangle ABC if you add the 52 to the 90 you’ll find the answer to be 142 if you subtract this then from 180 you’ll find 38 to be your answer

Therefore if you add the 38 the 52 and the 90 you’ll get 180

Based only on the information given in the diagram, it is guaranteed that Δ ABC ≅ Δ XYZ. It is true that Δ ABC ≅ Δ XYZ. Option A is correct.

What are the conditions of the congruent triangle?

Triangles that are equivalent in terms of size and form are known as congruent triangles.

It is certain that XYZ gave simply the facts in the diagram, traingle ABC, and XYZ is similar. It is true that triangles XYZ and ABC are similar.

The angle of triangles ABC and XYZ is;

∠A= 180° -(90+52) = 38°

∠B= 90°

∠C=38°

∠X=38°

∠Y=90°

∠Z=180° -(90+38°) = 52°

∠B =∠Y=90°

Based only on the information given in the diagram, it is guaranteed that Δ ABC ≅ Δ XYZ. It is true that Δ ABC ≅ Δ XYZ.

Hence, option A is correct.

To learn more about the congruent triangle refer;

https://brainly.com/question/12413243

#SPJ2

Find the slope of the line through the points(-4,-7) and (4,3)

Answers

Answer:

4/5

Step-by-step explanation:

The first point (-4, -7) lies in the third quadrant and the second one in the first quadrant.  This tells us immediately that the slope is positive; y increases as x increases.  The change in x is 4 - (-4), or 8; this is the 'run.'  The change in y  is 3 - (-7), or 10; this is the 'rise.'

Thus the slope of this line is m = rise/run = m = 8/10, or m = 4/5

Last year, 260 students went to the senior prom at M&T Bank Stadium. This year, the number of students who attended senior prom increased by 9%. How many students attend the senior prom at M&T Bank Stadium this year? Round you answer to the nearest whole number. ​

Answers

Answer:

283 people went this year to the stadium.

Step-by-step explanation:

Let's put this data into pieces so it's less overwhelming.

Last year 260 students went to the prom.

Currently the number of students who attended has increased by 9% from last year.

And the question is asking how many students attended this year?

Well, if this is increasing by 9%, wouldn't we just find 9% of 260 then add it to 260?

0.09 * 260 = 23.4

260 + 23.4 = 283.40. Obviously we can't have 40% of a human being, so let's round it to 283.

find the value of x, y, v and w​

Answers

Now,

x + 35° = 180° ( Co - interior angle )

x = 145°

Then,

y = x = 145° ( Vertically Opposite angle )

Again,

v + 43° = 180° ( Co - interior angle )

v = 137°

Then,

v + w = 180° (Co - interior angle )

137° + w = 180°

w = 180° - 137°

w = 43°

I hope it's help you...

Mark me as brainliest...

A typical serving of fish is 4 ounces. What is this serving size in grams?

Answers

Answer:

the answer is 113.398 grams

113.398 grams
4 ounces is 113.398 in grams

can you help me with this. Find the surface area ​

Answers

Answer:

2370 cm²

Step-by-step explanation:

2(32·15+15·15+15·32) = 2370

Select the graph that would represent the best presentation of the solution set.
|xl > 5

Answers

There isn’t a picture but I think the answer is the one in the picture I attached.

Please answer correctly to get brainliest

Answers

Answer:

Step-by-step explanation:

This is only my guess, as I haven’t done this topic in a few months

A. 398/427

0.93

B. 123/1192

0.10

C. 339/403

0.84

. A man travels 13km by bus , 8km by car and y km by train . If the man has to travel a total of 30 km , find y. *

Answers

Answer:

9km

Step-by-step explanation:

30-(13+8)=9km

I hope you understand

Can someone help

Write an equivalent expression for
63.62.65.6.

Answers

When multiplying the same number raised to different powers add the powers together.

3 + 2 + 5 = 10

Because you are also multiplying a value without a power you need to add 1 to the sum of the powers:

10 + 1 = 11

Answer: 6^11

Question 3 (Multiple Choice Worth 1 points)
(06.05 LC)
The two-way table shows the number of students in a school who like reading and/or gardening.
Like Reading
Do Not Like Reading
Total
Like Gardening
32
?
58
Do Not Like Gardening
19
23
42
Total
51
49
100
What is the missing number in the table?
16
19
26
0
90

Answers

Answer:

26

Step-by-step explanation:

Horizontally:

Like reading = 32

Do not like reading = ?

Total = 58

Total = Like reading + Do not like reading

Do not like reading = Total - Like reading

= 58 - 32

= 26

Do not like reading = 26

Vertically:

Like gardening =

Do not like gardening = 23

Total = 49

Total = Like gardening + Do not like gardening

Like gardening = Total - Do not like gardening

= 49 - 23

= 26

Like gardening = 26

Therefore,

The missing number in the table is 26

I will give BRAINLIEST to the correct answer
Find the measure of angle 6.

Answers

Answer:

m∠6 = 116°

Step-by-step explanation:

first find x:

7x - 17 = 2x + 78

subtract 2x from both sides: 5x - 17 = 78

add 17 to both sides: 5x = 95

divide by 5: x = 19

plug x into 7x - 17

7(19) - 17 = 116

∠6 and 7x - 17 are vertical angles and therefore congruent, so m∠6 also = 116°

Please help my teacher will kill me

Answers

1st image: 1, angle 1 is next to angle 2.
2nd image: since those angels are parrelled they’re the same number, so you just need to solve the equation.
6x+2=56
6x=54
6x/6 = 54/6
x=9

hope that helps!

Please help me I’ll mark as brainliest.

Answers

Answer:

Step-by-step explanation:

6x² + 108x + 707  = 5

Subtract 707 from both sides

6x² + 108x = 5 - 707

6x² + 108x = - 705

Divide the whole equation by 6

[tex]\frac{6x^{2}}{6}+\frac{108x}{6}= \frac{-702}{6}\\\\x^{2}+ 18x = - 117\\[/tex]

Divide 18 by 2 = 9

Add 9² to both sides

x² + 18x + 9² = -117 + 9²

x² + 18x  + 81 = -117 + 81

(x + 9)² = - 36

Answer:

(x + 9)^2 = -36

Step-by-step explanation:

6x^2 + 108x + 707 = 5

6x^2 + 108x = -702

x^2 + 18x = -117

x^2 + 18x + (18/2)^2 = -117 + (18/2)^2

x^2 + 18x + 81 = -117 + 81

(x + 9)^2 = -36

A farmhouse shelters 10 animals. Some are pigs and some are chickens. Altogether there are 30 legs. How many of each animal are there? PLSS HELP!!

Answers

Answer:

theres 5 pigs and 5 chickens

Step-by-step explanation:

5 pigs 4 legs 5x4=20

5 chickens and 2 legs 5x2=10

20+10=30

Find the surface area of a cylinder with a height of 10 inches and base diameter of 6 inches.
______ square inches​

Answers

244.92 is the surface area

Answer:

The surface area of cylinder is 244.92 inches²

hope it helps

have a nice day

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