Given f '(x) = (2 - x)(6 - x), determine the intervals on which f(x) is increasing or decreasing. (2 points)
Decreasing (-∞, 2); increasing on (6, ∞)
Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)
Decreasing (-∞, 2) U (6, ∞); increasing on (2, 6)
Increasing (-∞, -2) U (-6, ∞); increasing on (-2, -6)

Answers

Answer 1

Answer:

Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)

Step-by-step explanation:

To determine where [tex]f(x)[/tex] is increasing or decreasing, we set [tex]f'(x)=0[/tex] and check for the intervals.

We see that [tex]f'(x)=0[/tex] when either [tex]x=2[/tex] or [tex]x=6[/tex]. Therefore, we'll need to check the intervals [tex](-\infty,2)[/tex], [tex](2,6)[/tex], and [tex](6,\infty)[/tex]

For the interval [tex](\infty,2)[/tex], we can pick [tex]x=0[/tex] . This means that[tex]f'(0)=(2-0)(6-0)=(2)(6)=12>0[/tex], showing that [tex]f(x)[/tex] increases on the interval [tex](-\infty,2)[/tex]

For the interval [tex](2,6)[/tex], we can pick [tex]x=4[/tex]. This means that [tex]f'(4)=(2-4)(6-4)=(-2)(2)=-4<0[/tex], showing that [tex]f(x)[/tex] decreases on the interval [tex](2,6)[/tex]

For the interval [tex](6,\infty)[/tex], we can pick [tex]x=7[/tex]. This means that [tex]f'(7)=(2-7)(6-7)=(-5)(-1)=5>0[/tex], showing that [tex]f(x)[/tex] increases on the interval [tex](6,\infty)[/tex]

Therefore, [tex]f(x)[/tex] is increasing on [tex](-\infty,2)\cup(6,\infty)[/tex] and is decreasing on [tex](2,6)[/tex].


Related Questions

how to make chicken, with rice ....​

Answers

Answer:

put rice with chicken

Step-by-step explanation:

basically how to write y-3=4(x+2) in slope intercept form

Answers

Answer: y = 4x + 11

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Rewrite in slope-intercept form.

Simplify the right side.

Simplify 4(x + 2).

y - 3 = 4x + 8

Move all terms not containing y to the right side of the equation.

Add 3 to both sides of the equation.

y = 4x + 8 + 3

Add 8 and 3.

y = 4x + 11

Your Welcome! :)

Simplify
O A. 6^16
O B. 6
O C. 6^4
O D. 1/6

Answers

the answer for this question is B

in simplest terms: (-5x-7)-(-4x-6)(−5x−7)−(−4x−6)

Answers

Answer:

-20x^2-59x-43

Step-by-step explanation:

a coffee mug collection includes four red mugs, eight yellow mugs and two white mugs. What is the probability of selecting two white mugs one after another?

Answers

Assuming that the selection process was done without replacement, the probability of selecting two white mugs without replacement is 1/28

Given data

Sample Space

Red mugs = 4

yellow mugs = 8

white mugs = 2

Sample Size = 4+8+2 = 14

We are going to assume the selection was done with out replacement

Hence the probability of selecting the first white mug is

Pr(W1) = 2/8 = 1/4

The probability of selecting the second white mug is

Pr(W2) = 1/7

Hence the probability of selecting  two white mugs one after another

= 1/4*1/7

=1/28

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10. Which of the following is the best financial situation?

Answers

Answer:

Having enough to retire.

Step-by-step explanation:

The biggest long-term financial goal for most people is saving enough money to retire. The common rule of thumb that you should save 10% to 15% of every paycheck in a tax-advantaged retirement account like a 401(k) or 403(b), if you have access to one, or a traditional IRA or Roth IRA.

Find the equation of a line that intersects with y=2x-1 on the y-axis and is parallel to y=-x. Please explain.

Answers

Answer:

so where does that line intersect the y axis? just plug in x=0 and you see y= -1. so (0, -1)

y = -x -1 is parallel because it has the same slope and goes through the right point

Creshawna has $52 in her bank account. She sells a few of her games and makes $134. She deposits that amount into her bank account. How much money does Creshawna have in her bank account after she deposits $134?

$180
$186
$190
$196

Answers

I'm pretty sure it's $186

Show that the equation y + 2 = 2(2x + 1) is linear and that it represents a proportional relationship between x and y.

Answers

y + 2 = 4x + 2
i hope thats right

Assume running consumes 93 calories per mile. If you run 8 - minute miles, what is your average power output, in watts?

Answers

774 watts so what he said is right

Average power output, in watts = 0.8103 watts

What is average power?

The average power represents the constant energy that has been used throughout the time of the journey at a constant rate.

It can be expressed by the following relation:

P=E/T

Given,

Energy consumed per mile = 93 calories

Time taken to cover 1 mile = 8 minutes

Energy consumed per minute = 93/8 calories

Average power = 93/8 = 11.625 calorie per minute

1 calorie per minute = 0.0697 watt

Average power output in watts = 11.625 × 0.0697

                                                    = 0.8103 watt

Hence, 0.8103 watt is the average power output in watt.

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can someone please find the slope for this?

Answers

The gradient is 1/4.

As you take two points the line passes though, then use the rise/run equation to find the slope or gradient

Find the points on x^2+3(y-2)^2 = 27
which are closest to and farthest from the origin

Answers

[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.

Let be a curve of the form [tex]x^{2}+3\cdot (y-2)^{2} = 27[/tex]. The distance with respect to origin is found by using the following Pythagorean identity:

[tex]r = x^{2}+y^{2}[/tex] (1)

Where [tex]r[/tex] is the square distance function.

We can modify (1) as following:

[tex]r = [27-3\cdot (y-2)^{2}]+y^{2}[/tex]

[tex]r = 27-3\cdot (y^{2}-4\cdot y +4)+y^{2}[/tex]

[tex]r = 27-3\cdot y^{2}+12\cdot y -12 + y^{2}[/tex]

[tex]r = -2\cdot y^{2}+12\cdot y+27[/tex] (1b)

Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:

First derivative test

[tex]-4\cdot y +12 = 0[/tex]

[tex]y = 3[/tex]

Second derivative test

[tex]r'' = -4[/tex]

The y-component represents a maximum.

Now we graph the function with the ressource of a graphing tool, we find the following points:

Farthest points: [tex](-4.89, 3)[/tex], [tex](4.89, 3)[/tex].

Closest points: [tex](0, -1)[/tex].

[tex](-4.89, 3)[/tex] and [tex](4.89, 3)[/tex] are the farthest from the origin and [tex](0, -1)[/tex] is the closest from the origin.

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PLS HELP!!!
Express each of these numbers, as a product of two fractions
1/15

Answers

[tex]\dfrac 13 \times \dfrac 15 = \dfrac 1{15}[/tex]

The product of the two fraction numbers whose result is 1/15 will be 1/3 and 1/5.

What is Algebra?

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The result of the product of the two fraction numbers is given below.

1/15

The factor of the number 15 is given as,

15 = 3 x 5

Then the expression is written as,

1/15 = 1/ (3 x 5)

1/15 = (1/3) x (1/5)

The multiplication of the two rational numbers whose result is 1/15 will be 1/3 and 1/5.

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Write an equation of each sentence. Use n to represent the unknown number. You can use the back page for your solution. (2 points each) 11. Six increased by a number is twenty. 12. A number decreased by seven is four. 13. The sum of two consecutive numbers is thirty-one. 14. The sum of twice a number and two is thirteen. 15. One less than a number is eighteen. 16. The square of a number increased by four is twice the number. 17. Twice a number is one-half. 18. The product of a number and its half is eighteen. 19. The average of a number and ninety is seventy. 20. Two more than a number is twelve.

PLEASE HELP Me​

Answers

Answer:11. 6 + n = 2012. n - 7 = 2013. n + n + 1 = 3114. 2n + 2 = 1315. n - 1 = 18 16. n² + 4 = 2x17. 2n = 1/218. n²/2 = 1819. n/2 + 90/2 = 7020. 2 + n = 12

Hoped this helped.

[tex]-BrainaicUser1357-[/tex]

Let the number be x

#11

[tex]\\ \sf\longmapsto x+6=20[/tex]

#12

[tex]\\ \sf\longmapsto x-7=4[/tex]

#13

[tex]\\ \sf\longmapsto x(x+1)=31[/tex]

#14

[tex]\\ \sf\longmapsto 2x+2=13[/tex]

#15

[tex]\\ \sf\longmapsto x-1=18[/tex]

#16

[tex]\\ \sf\longmapsto x^2+4=17[/tex]

#17

[tex]\\ \sf\longmapsto x^2/2=18[/tex]

#18

[tex]\\ \sf\longmapsto x+90/2=70[/tex]

Description of a turn for those who have never done math / for a child​

Answers

Answer:

Step-by-step explanation:

1+1=2

2+2=4

3+3=6

4+4=8

5+5=10

Figures A and B at right are similar. Assuming that figure A is the original figure, find the scale factor and find the lengths of the missing sides of figure B.

A 4 sided polygon, labeled A, with sides labeled as follows: left, 15, top, 12, right, 18, bottom, 20. A smaller, 4 sided polygon, labeled b, oriented the same way, has left side labeled: 3.

Answers

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

How to find Scale Factor?

Scale factor = dimension of new figure / dimension of original figure

The polygons given are shown in the diagram attached below.

Figure A is the original figure

Figure B is the new figure.

x, y, and z has been used to mark the missing sides of figure B.

One dimension of original figure = 15

Corresponding dimension of the new figure = 3

Scale factor = new/original = 3/15

Scale factor = 1/5

To find the missing sides of figure B, multiply each corresponding side lengths of Figure A by the scale factor:

x = 12 × 1/5 = 2.4

y = 18 × 1/5 = 3.6

z = 20 × 1/5 = 4

In summary:

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

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A rectangle is 8 feet long. Its width is represented by “seven plus x feet.” Which expression represents the area, in square feet, of the rectangle?

Answers

56 + 8x

Area of Rectangle = Length x Width

Area of Rectangle = 8(7 + x)

Solve for x: one over four (4x + 15) = 24

A: 45
B: 207/4
C: 81/4
D: 9

Answers

Answer:

[tex]C. x = \frac{81}{4} = 20.25[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}\left(4x+15\right)=24[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}4[/tex]

[tex]4\cdot \frac{1}{4}\left(4x+15\right)=24\cdot \:4[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x+15=96[/tex]

[tex]\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}[/tex]

[tex]4x+15-15=96-15[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x=81[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]

[tex]\frac{4x}{4}=\frac{81}{4}[/tex]

[tex]Simplify[/tex]

[tex]x=\frac{81}{4}[/tex]

Determine if the sequence below is arithmetic or geometric and determine the common difference/ ratio in simplest form

15, 11 ,7, …

Answers

Answer:

This is the arithmetic sequence which has a common difference that equals to -4.

Step-by-step explanation:

An arithmetic sequence is a sequence with common difference. A common difference can be found by subtracting previous term with next term.

A common difference can be expressed in [tex]\displaystyle \large{d=a_{n+1}-a_n}[/tex] where d stands for common difference.

________

Moving to the question given. We have a sequence with given 15,11,7, ... first subtract 15 with 11.

11-15 = -4

7-11 = -4

Therefore, we can conclude that the common difference is -4 thus making the given sequence an arithmetic.

Let me know if you have any question so regarding the sequence!

Ilana has 70¢ in her purse. All the coins have the same value. What could describe all the coins she has in her purse?

71 pennies
8 dimes
14 nickels
3 quarters

Answers

Answer:

14 nickels is the answer

Step-by-step explanation:

What does it mean to be an independent student? A. You must pick your own study topics and research them. B. You can set your own deadlines, within a fixed time frame. C. You are responsible for your own study schedule and organization. D. You are expected to work without extra help from a teacher or tutor.

Answers

Answer:

C

Step-by-step explanation

It makes the most sense

Answer:

check online for more information

Two side of a triangle have the following measures.

Answers

Answer:

add the two then subtract the two and put those answers in each box :)

Step-by-step explanation:

hope this helped! happy holidays!

Seven values on the number line above are marked with letters. Which letters represent integers?

Answers

B C L Abecause I did this it’s weird but you have to trust me

If x = 9, what is the value of 6(x - 2)?

Answers

Answer: 42

6(9-2)

= 6 * 7

= 42

Answer:

6(9-2)

=6×7

=42 ans

Step-by-step explanation:

I think it help you I also you understand it

In the New York marathon there were 45 360 runners. 7 /10 of the runners were women. How many of the runners were men? ​

Answers

Answer:

13,608

Step-by-step explanation:

If 7/10 of the runners were women, than 3/10 of the runners were men. 3/10 of 45,360 runners is 13,608.

Hope this helps! Pls give brainliest! Also, plz sub to kgirl633 on yt.

A line includes the points (-7, 1) and (7, -1). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=-1/7x

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-1)/(7-(-7))

m=-2/(7+7)

m=-2/14

simplify

m=-1/7

--------------------

y-y1=m(x-x1)

y-1=-1/7(x-(-7))

y-1=-1/7(x+7)

y=-1/7x-7/7+1

y=-1/7x-1+1

y=-1/7x

What fraction equals 15/21 with a denominator of 7

Answers

Answer:

5/49

Step-by-step explanation:

decimal form = 0.10

Answer:

5/49

hope it helps! stay safe as always!

Divide £121 in the ratio 2:9.

Answers

is this one of your answer choice?

A line that includes the point (0, -2) has a slope of 1. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=1x-2

Step-by-step explanation:

Well this one is already given

When x=0, it's the y intercept

and it gives the slope, so we got it :D

Answer:

y=x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=1(x-0)

y+2=1(x)

y+2=x

y=x-2

write an expression to represent admission to a zoo of $10.00 and the cost of special exhibits s at $4 each. Evaluate you expression when s=2

Answers

Answer:

10.00 +4s .

u wanted expression ,  not answer.?

Step-by-step explanation:

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