F(x)= 6•(1/3) x graph the function khan academy

a. The function f is increasing on the intervals (-3 0) and (3, ∞).

The function f is decreasing on the intervals (-∞, -3) and (0, 3)

b. the local extreme values of the function occur at x = -3 and x = 3

To find where the function is increasing or decreasing, we need to analyze the first derivative of the function and its critical points.

a. The function is increasing on the open interval(s) when its first derivative is positive, and it is decreasing on the open interval(s) when its first derivative is negative.

Given the function f(x) = x⁴ - 18x² + 81

first derivative = 4x³ - 36x

critical points

4x³ - 36x = 0

4x(x² - 9) = 0

x = 0, x = -3, and x = 3.

the intervals of increasing and decreasing

For x < -3,

say x = -4

f'(-4) = 4(-4)³ - 36(-4) = -256 + 144 = -112 (negative)

For -3 < x < 0

say x = -1

f'(-1) = 4(-1)³ - 36(-1) = -4 + 36 = 32 (positive)

For 0 < x < 3,

pick x = 1

f'(1) = 4(1)³ - 36(1) = 4 - 36 = -32 (negative)

For x > 3,

say x = 4

f'(4) = 4(4)³ - 36(4) = 256 - 144 = 112 (positive)

Based on the above analysis, we have that:

The function f is increasing on the intervals (-3 0) and (3, ∞).

The function f is decreasing on the intervals (-∞, -3) and (0, 3)

b. To identify the function's local extreme values, we look for critical points that correspond to local maximum or minimum.

From the graph we can see that the local minimum is at x = -3 and x = 3

Learn more about local minimum at

https://brainly.com/question/2437551

#SPJ1

Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

Based on the rate at which all three computers process bills, the time taken for the computers to process 1,780 bills is 4 minutes.

First find the number of bills left when the third computer joined:

= 1,780 - (160 x 1.5 mins) - (160 x 1.5 mins)

= 1,300

Then the average speed of all three computers is:

= 160 + 160 + 200

= 520 bills per minute

The time taken to finish up the other bills would be:

= 1,300 / 520

= 2.5 minutes

Add this to the minutes already elapsed before the third computer was used:

= 2.5 + 1.5

= 4 minutes

Find out more on rate of work at https://brainly.com/question/24482367.

Answer: C

Step-by-step explanation: The answer is C because it is.

Answer:

55 ft.

Step-by-step explanation:

First find the area of Lot X

67 • 70 = 4,690

Subtract the are of Lot X from the total area

8,375 - 4,690 = 3,685

3,685 is the area of Lot Y

Now divide 3,685 by the length of Lot Y : 67

3,685 ÷ 67 = 55

The width of Lot Y is 55 ft.

Hope this helps!

Answer:

84

Step-by-step explanation:

i used  a calculator and its the answer

Answer:

A. 28 miles

Step-by-step explanation:

12/3=4 miles per hour

4x7=28

4mphx7hours=28 miles

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

For more such question on monopolist. visit :

https://brainly.com/question/28336090

#SPJ8

\(x=2y\) and \(x=y^3\) intersect when

\(2y=y^3\implies y^3-2y=y(y^2-2)=y(y-\sqrt2)(y+\sqrt2)=0\)

\(\implies y=0\text{ or }y=\sqrt2\text{ or }y=-\sqrt2\)

We omit the negative root, since we only care for \(y\ge0\).

In the interval (0, √2), we have \(y^3<2y\). Then the volume is given by the integral

\(\displaystyle\pi\int_0^{\sqrt2}(2y)^2-(y^3)^2\,\mathrm dy=\pi\int_0^{\sqrt2}4y^2-y^6\,\mathrm dy\)

and so the volume is (32√2)/21 π.

Answer:

Length = 10 cm

Width = 10-2 = 8 cm

Step-by-step explanation:

Area formula (L)(W)

80 = 10(x-2)

80 = 10x - 20

Add 20 to both side

100 = 10x

x= 10

Length = 10 cm

Width = 10-2 = 8 cm

Answer: 40.27

Step-by-step explanation:

Let their September bill be x

Therefore, the October bill will be = x - 3.87.

Therefore, the addition of both bills will be:

x + (x - 3.87) = 237.75

x + x - 3.87 = 237.75

2x - 3.87 = 237.75

2x = 237.75 + 3.87

2x = 241.62

x = 241.62/2

x = 120.81

Therefore, September bill was 120.81

Since the 3 students share the bull equally, the amount owed by each will be:

= 120.81 / 3

= 40.27

Each person owes 40.27

Answer:

$90.00

Step-by-step explanation:

40% of What is 36?

40/4 = 10 (10%)

36/4 = 9 (9 is 10% of the answer we are looking for)

Multiply both answers (9 and 10) by each other.

You get 90

The width of the canyon in the given image is 70 ft wide.

To find the width of the canyon, we can visually extend side DC and AE to form two sides of a rectangle.

Given that side DC is the same as side AE (80 ft), we can use this same reasoning to determine that the width is the sum of side AB and side BC, which is 35 + 35.

This gives us a width of 70 ft.

In a rectangle, the longer side is known as the length and the shorter side is known as the width.

Therefore, using the sum of side AB and side BC, we get a width of 70 ft for the canyon.

Read more about width here:

https://brainly.com/question/25292087

#SPJ1

Answer:

$233.95

Step-by-step explanation:

299 x 0.7 = 209.30

209.30 x 1.07 = 233.95

Answer:

sample mean:: 17.92

ME = z*s/sqrt(n) = 1.8807*6.35/sqrt(47) = 1.7421

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

Step-by-step explanation:

Step-by-step explanation:

4/5 gallons for 280 ft² (the ² is missing in the question ...).

3 gallons would be 15/5.

so, what do I need to multiply 4 with to get 15 ?

4×x = 15

x = 15/4

multiplying now also 280 ft² with this factor gives us the answer :

280 × 15/4 = 70 × 15 = 1050 ft²

they can paint 1050 ft² with 3 gallons of paint.

Step-by-step explanation:

work he in a department store

To find the area of the triangle, we will use the formula below:

where b is the base

h is the height

A is the area of the triangle

From the question,

b = 10 and h = 6

substitute the value into the formula and evaluate

Step-by-step explanation:

When dividing by a negative number, you "flip" the inequalities sign so you would divide -20 by -2 which would leave you with 10. X is left where it is and you flip the inequalities sign to a ≥ sign.

final answer =

x ≥ 10

Answer:

A

Step-by-step explanation:

All quadrilaterals have a total of 360° for the interior angles

X = 360 - (125+95+105) = 360 - 325 = 35°

Answer:

0.375

Step-by-step explanation:

3/2 equals 1 and a half, and 1 and a half divided by 4 will get you 0.325

Answer:

4x - 2 = 3x + 1. Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member. 4(3) - 2 = 3(3) + 1.

Answer:

Equation: y =  \(\frac{1}{5}\)x - 1

Slope: \(\frac{1}{5}\)

Y-intercept: -1

Step-by-step explanation:

Point 1: (0, -1) or (\(x_{1}\), \(y_{1}\))

Point 2: (5, 0) or (\(x_{2}\), \(y_{2}\))

Slope:

\(y_{2}\) - \(y_{1}\) / \(x_{2}\) - \(x_{1}\)

0 - (-1) / 5 - 0

\(\frac{1}{5}\) = m

Equation:

y - \(y_{1}\) = m (x - \(x_{1}\))

y - (-1) = \(\frac{1}{5}\) (x - 0)

y + 1 =  \(\frac{1}{5}\)x

y =  \(\frac{1}{5}\)x - 1

Y-intercept:

-1

Answer:

-4/9*3/2

-4*3/9*2

-12/18

-2/3

Answer:

-2/3

Step-by-step explanation:

-4/9 divided by 2/3

you turn divided into multiplied and flip the second number

-4/9*3/2

you can cross multiply.

once you have simplified you should have

-2/3*1/1

simplified further to

-2/3*1

so,

-2/3 is the answer :)

The length of a rectangle is 55  inches and the width of the rectangle is  17 inches

Given that The length of a rectangle is four more than triple the width.  If the perimeter is 144 inches and asked to find the dimensions of the rectangle

Length of a rectangle = 4 + triple the width

Let's assume the length of a rectangle is "l" and the width is "b"

l= 4 + 3b

perimeter of rectangle =2 ( l +b )

perimeter of rectangle = 2 ( 4 +3b +b)

perimeter of rectangle = 2 ( 4 + 4b )

Given that perimeter of rectangle = 144 inches

144 inches =  2 ( 4 + 4b )

72 inches = 4 + 4b

b= 17 inches

l= 4 + 3b

l=4+51

l=55 inches

Therefore the dimensions of rectangle are 55 inches and 17 inches

Hence,The length of a rectangle is 55  inches and the width of the rectangle is  17 inches.

Learn more about rectangle here:

https://brainly.com/question/15019502

#SPJ9

Answer:

we, don't know

Step-by-step explanation:

sorry! You can ask experts

Answer:

$ 190

Step-by-step explanation:

To find the answer you add $112.65 , $29.75 and $48.33.

The answer then becomes $190.73

That means approximetely he spent because $ 190 is closer to $190.73 than $170 , $210 and $ 230.

answer is $190

HOPE THIS HELPED

Answer:

190$

Step-by-step explanation:

add them all together

The critical value value needs to be lower than the calculated or obtained value (test statistic) to reject the null hypothesis

What is Null Hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Reason:

Critical value < calculated or obtained value (test statistic) to reject the null hypothesis

We are unable to reject the null hypothesis if the statistic is less than or equal to the crucial threshold (e.g. no effect). If not, it is turned down. This interpretation can be summed up as follows: Critical Value = Test Statistic fail to invalidate the statistical test's null hypothesis.

If the test statistic is less than the crucial value in a lower-tailed test, the decision rule requires that the investigators reject H0. If the test statistic in a two-tailed test is extreme—either bigger than an upper critical value or smaller than a lower critical value—investigators are required by the decision rule to reject H0.

To learn more about Null Hypothesis visit:

brainly.com/question/28920252

#SPJ4

Answer:

7% = .07 = \(\frac{7}{100}\)

Step-by-step explanation: