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

Angle wxz is congruent to angle zxy. Find the value of X

Answers

Answer:

  x = 18

Step-by-step explanation:

Congruent angles have equal measures.

  74° = (4x +2)°

  72 = 4x . . . . . . divide by °, subtract 2

  18 = x . . . . . . .  divide by 4

How to find the derivative???

Answers

[tex]e^{2x} = \ln(y^3)\\\\\implies e^{2x} = 3 \ln y\\\\\implies \dfrac{d}{dx} e^{2x} = 3\dfrac{d}{dx}( \ln y)\\\\\implies 2e^{2x} = 3 \cdot \dfrac 1y \cdot \dfrac{dy}{dx}\\\\\implies 3\dfrac{dy}{dx} = 2ye^{2x}\\\\\implies \dfrac{dy}{dx} = \dfrac{2y}3 e^{2x}[/tex]

Joyce drives from Louisville to St. Louis which is 260 miles in 4 hours. How many miles can she drive in 10 hours

Answers

650 miles!!!!!!!!!!!!!!

Answer:

260 miles in 4 hours equals (260 / 4) = 65 miles per hour

In 10 hours she can drive 650 miles

Step-by-step explanation:

A line with a slope of 2 passes through the point (3,9).
Write an equation for this line in point-slope form.

Answers

Answer:

y-9=2(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-9=2(x-3)

brainless for the person who gets this right!
which expression its equivalent

Answers

D

If we expand the parentheses, and multiply everything inside with everything outside, we get

4•6x + 4•11
Which is equal to 24x + 11

1
Renee is comparing prices from Kay's Catering and Weddings 'R' Us to serve the meals for her wedding
dinner. The catering cost, c, for each catering service Renee is considering, based on x meals served, is
shown on the coordinate grid.
Catering Cost for Wedding
2000
1800
1600
Kay's Catering
A
1400
1200
1000
C= 10m + 800
C = 15m + 400
Catering Cost ($)
800
Weddings 'R' US
B
C =
600
5m + 800
am + 800
400
200
C=
10 20 30 40 50 60 70 80 90 100
Number of Meals
с
C= 800m + 10
C = 400m + 15
Which system of equations is best represented by this graph?
D
C = 3m + 1,600
C =
M + 80

Answers

Answer:

5000

Step-by-step explanation:

I NEED HELP!!!!!
4. Three bags of Skittles and two bags of M&M's
weigh 3 pounds. Four bags of Skittles weigh 3
pounds. All bags of skittles weigh the same, and
all bags of M&M's weigh the same. What is the
ratio of the weight of a bag of Skittles to a bag of
M&M's?

Answers

Answer:

Step-by-step explanation:

How many Skittles is in a 4 pound bag?

Fun-size packages are perfect for parties, party favors, trick-or-treaters, gift baskets, lunch treats and on-the-go snacks. Approximately 20 individual packs per lb.

...

Skittles Fun-Size Packs, 4-Lb Box.

Aarón rides his bike away from home at a constant speed he stops at the park for a while before riding back home at a constant speed

Answers

Answer:

Step-by-step explanation: This is the answer

if 5a+b=14 then a = what
explain how you got it pls

Answers

Answer:

[tex]a = \frac{14 - b}{5}[/tex]

Step-by-step explanation:

The rule to know and follow is:

You can add, subtract, multiply or divide by anything so long as the same thing is done to both sides of the equals sign;

5a + b = 14

If we want to get: "a = ...", then we use the rule to isolate the variable a on one side of the equation;

Firstly, we subtract b from both sides:

5a + b - b = 14 - b

5a = 14 - b

Then, divide both sides by 5:

[tex]\frac{5a}{5} = \frac{14 - b}{5} \\\\ a = \frac{14 - b}{5}[/tex]

The refrigerator is priced at $525.50. There is a 6% sales tax rate. What is the sales tax for the refrigerator in dollar and cents?

Answers

Answer:

$31.53

31 dollars 53 cents

Step-by-step explanation:

6% is equal to 0.06.

0.06 * 525.50 = 31.53.

Hope this helps

Jeremiah buys 6 tacos and 8 enchiladas for 60 dollars. Kennedy buys 3 tacos and 2 enchiladas for 18 dollars.

Answers

Answer:

What's the question lol

charles had a sheet cake for his birthday when 9/12 remained charles took 1/3 of the remaining cake to wrap and save for later what fraction of the original cake did he wrap

Answers

Answer:

He wrapped 3/4 of the cake.

Step-by-step explanation:

1/3 of 9/12 is 0.25 and 0.25 converted into a fraction is 3/4

- Hope this helps!

Learning Task 1: Write the fraction of each shaded figure. Find the sum. Write your answer in your notebook.

Please is anyone can help me​ please

Answers

Learning task 1

1. 3. 3. 1.

4. 2

2. 5. 4. 6.

9. 13

5. 3. 6. 7.

5. 9

Step by step explanation:

hopefully that's help

A triangle has two angles with measures of 50 degrees and 70 degrees joined by a side with a length of 20 centimeters.
Which figure represents this triangle?
709
50
O
20
50
2009
70
o
500
709
20
20
70°
50°

Answers

Answer:

Step-by-step explanation:

Given :-

Two angles in a triangle have measurements of 20° and 50 °.

To Find  :-

Measurement of third angles of triangle

Solution :-

We know that the sum of all angles of triangle is 180°.

Measurement of third angles = x

20° + 50° + x = 180°

combine like terms

70° + x = 180°

subtract both sides from 70°.

70° - 70° + x = 180° - 70°

x = 110 °

Hence, the measurement of the third angie of a triangle is 110°.

Answer:

The third option is the correct answer.

Latex paint sells for $21 per gallon and will cost you $210 to paint your room. If each gallon will cover 300 square feet, how many square feet of wall space do you have in your room?

square feet

Answers

Answer: 3000 square feet

Step-by-step explanation: 21x10=210 .     300x10=3000

Solve the evens and I will mark you brainliest when available.

Answers

Answer:

The solution is in the photo

Hemp bell bell help math

Answers

Answer:

This is indeed a function!

Step-by-step explanation:

Find the slope of the line on the graph. Write your answer as a fraction or whole number, but a mixed number or decimal.

Answers

Answer:

-1/4

Step-by-step explanation:

Rise over run

Rises -1 runs 4

slope = -1/4

Susan loaned Marcel $19,080 at an interest rate of 17% for 5 years. How much will Marcel pay Susan at the end of 5 years? Round your answer to the nearest cent, if necessary.

Answers

3,243.6 will be the 17% interest rate of the 5 years so 3,243.6+19,080= 22,323.6

Manny has a garden that is 12 feet long and 9 feet wide. What is the perimeter of
Manny's garden?
Use the formula for perimeter, P =
2 (1 + w).
432 feet
O 33 feet
O 42 feet
216 feet

Answers

Answer:

42 ft

Step-by-step explanation:

2(L + W ) = P

2 (12 + 9) = P

2 (21) = P

42 = P

P = 42


1) Use the distributive property to write an expression that is equivalent to 8(a + 4).
8(a + 4) = _a + _

Answers

8a + 32
Distribute the 8 to each term in the parentheses.

Solve two eighths times four fifths

Answers

1/5 is the answer if you taking about 2/8 times 4/5

Answer:

8/40 or 1/5

Step-by-step explanation:

2x4=8

8x5=40

That gives us the answer of 8/40 but if you need simplifying just divide 8/40 by 8/8 and you will get the final answer of 1/5

A price was decreased by 12%. Then it was increased by an additional 5%. What is the percent of the total decrease?

Answers

Answer:

7.6%

Step-by-step explanation:

First the decrease

(100-12)%=88%

then the increase

(88)(1.05)=92.4%

The total decrease

(100-92.4)% = 7.6%

Hope this helps

Solve the following equation 2x-17=-53

Answers

Step-by-step explanation:

2x - 17 = - 53

2x = - 53 + 17

2x = - 36

x = - 36/2

x = - 18

Answer:

x = -18

Step-by-step explanation:

2x - 17 =  -53

    +17 = + 17            Add 17 to both sides

2x       =   -36            

  x = -36 ÷ 2           Divide by 2

   x = -18

I need help on my homework.

Answers

Answer:

[tex] \frac{3}{4} > \frac{ - 2 + 2x}{4} \\ \\ (4 \times) \frac{3}{4} > \frac{ - 2 + 2x}{4} ( \times 4) \\ \\ 3 > - 2 + 2x \\ \\ 3 + 2 > - 2 + 2 + 2x \\ \\ 5 > 2x \\ \\ 5 \div 2 > 2x \div 2 \\ \\ \frac{5}{2} > x \\ \\ x < \frac{5}{2} [/tex]

I hope I helped you^_^

I want a way to solve this question​

Answers

Answer:

Step-by-step explanation:

[tex]cos~L=\frac{m^2+n^2-l^2}{2mn} \\=\frac{5^2+8^2-7^2}{2*5*8} \\=\frac{25+64-49}{80} \\=\frac{40}{80} \\=\frac{1}{2} \\=cos 60\\[/tex]

∠L=60°

find the value of X in the following figures​

Answers

Answer: 70

Step-by-step explanation:

Diagonals of a rhombus bisect each other at right angles, so

[tex]x+20=90\\\\x=\boxed{70}[/tex]

The graphs below have the same shape. What is the equation of the blue graph?
G(x) =
O A. G(X) = x^2 + 1
O B. G(X) = (x - 1)^2
O C. G(X) = (x + 1)^2
O D. G(x) = x^2-1

Answers

Answer:

c) G(x) = (x + 1)**2

Step-by-step explanation:

A function left shift is x + shift and a right shift is x - shift.


5cm
10cm
Q
Q2
Q3
Referring to the diagram above.
if Q1 = 9.0 uC, Q2 = -5.0 uC and Q3 = 32.0 uc,
what is the magnitude of the electric field at Q2, due to Q1 and Q3?

Answers

Answer:
I’m pretty sure it 15cm
Step by step

factorise
18p+6
please im so bad​

Answers

ANSWER: 18p+6= 6(3p+1)
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