Can anybody help plzz?? 65 points

Can Anybody Help Plzz?? 65 Points

Answers

Answer 1

Answer:

[tex]\frac{dy}{dx} =\frac{-8}{x^2} +2[/tex]

[tex]\frac{d^2y}{dx^2} =\frac{16}{x^3}[/tex]

Stationary Points: See below.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Calculus

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

[tex]f(x)=\frac{8}{x} +2x[/tex]

Step 2: Find 1st Derivative (dy/dx)

Quotient Rule [Basic Power]:                    [tex]f'(x)=\frac{0(x)-1(8)}{x^2} +2x[/tex]Simplify:                                                      [tex]f'(x)=\frac{-8}{x^2} +2x[/tex]Basic Power Rule:                                     [tex]f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}[/tex]Simplify:                                                     [tex]f'(x)=\frac{-8}{x^2} +2[/tex]

Step 3: 1st Derivative Test

Set 1st Derivative equal to 0:                    [tex]0=\frac{-8}{x^2} +2[/tex]Subtract 2 on both sides:                         [tex]-2=\frac{-8}{x^2}[/tex]Multiply x² on both sides:                         [tex]-2x^2=-8[/tex]Divide -2 on both sides:                           [tex]x^2=4[/tex]Square root both sides:                            [tex]x= \pm 2[/tex]

Our Critical Points (stationary points for rel max/min) are -2 and 2.

Step 4: Find 2nd Derivative (d²y/dx²)

Define:                                                      [tex]f'(x)=\frac{-8}{x^2} +2[/tex]Quotient Rule [Basic Power]:                  [tex]f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2[/tex]Simplify:                                                    [tex]f''(x)=\frac{16}{x^3} +2[/tex]Basic Power Rule:                                    [tex]f''(x)=\frac{16}{x^3}[/tex]

Step 5: 2nd Derivative Test

Set 2nd Derivative equal to 0:                    [tex]0=\frac{16}{x^3}[/tex]Solve for x:                                                    [tex]x = 0[/tex]

Our Possible Point of Inflection (stationary points for concavity) is 0.

Step 6: Find coordinates

Plug in the C.N and P.P.I into f(x) to find coordinate points.

x = -2

Substitute:                    [tex]f(-2)=\frac{8}{-2} +2(-2)[/tex]Divide/Multiply:            [tex]f(-2)=-4-4[/tex]Subtract:                       [tex]f(-2)=-8[/tex]

x = 2

Substitute:                    [tex]f(2)=\frac{8}{2} +2(2)[/tex]Divide/Multiply:            [tex]f(2)=4 +4[/tex]Add:                              [tex]f(2)=8[/tex]

x = 0

Substitute:                    [tex]f(0)=\frac{8}{0} +2(0)[/tex]Evaluate:                      [tex]f(0)=\text{unde} \text{fined}[/tex]

Step 7: Identify Behavior

See Attachment.

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

Can Anybody Help Plzz?? 65 Points

Related Questions

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Step-by-step explanation:

Answer:

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There were 42 mangoes in each crate. 12 such crates of mangoes were delivere to a factory. 4 mangoes were rotten and had to be thrown away. The remaining mangoes were packed into boxes of 10 mangoes each. How many mangoes were left after the 4 rotten ones were thrown away? * Your answer​

Answers

Answer: 50

Step-by-step explanation: 42x12=504. 504-4=500. 500/10=50.

Answer:

Total Mangoes = 50

Rotten =  46

Step-by-step explanation:

50 divided by 10 = 5.

50 minus 4 is 46.

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Answers

Answer:

y=3/7x+46/7

Step-by-step explanation:

Parallel lines have the same slope. This means in the equation y=mx+b, m=3/7 for sure. Then, it gives us the point (1,7). The line has to go through this point so we plug it in: 7=3/7(1)+C. Then, we solve for C using algebra.

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what is the value of q in the equation 4/5q = 32

Answers

Answer:

40

Step-by-step explanation:

4/5 * q = 32

First you divide 4/5 by itself so you can eliminate it from the equation and then you have to divide 32 by 4/5 n when you do that you get 40. So q = 40.

5, 18, 6, 18, 13 WHATS THE INTERQUARTILE RANGE??

Answers

Answer: 12.5

Step-by-step explanation:

25th Percentile: 5.5

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Who can't wait for Cyberpunk to come out

Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

0.2hrs/dollars

Step-by-step explanation:

Given parameters:

Cost of bike = $31

Time duration  = 6hrs

Unknown:

Hours customers get per dollar = ?

Solution:

The number of hours customer gets per dollar is;

      Number of hrs/dollar = [tex]\frac{time duration }{cost}[/tex]

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Answers

Answer:

x= -1

Step-by-step explanation:

Distribute:

2(x -5) -6 = -18

2x -10 -6 =-18

Subtract the numbers:

2x -10 -6 =-18

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Add 16 to both sides of the equation:

2x =16 += -18

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2x = -2

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x=-1

Answer:

x = -1

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Answers

Answer:

8.026, 8.062, 8.26, 8.6

Step-by-step explanation:

Answer:

Hi! I'm happy to help!

Step-by-step explanation:

8.026, 8.062, 8.26, 8.6

PLease help me for my homework hahaqhahahahahhahaha please

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Answer

Step-by-step explanation:

rise over run so it'd be 3/3 positive or y= 3x-3

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Answer:

300+ 50 + 2

Step-by-step explanation:

If you add 300+50+2 you get 352 all you need to do is break down the number to pieces! :)

Answer: 300 + 50 + 2

Explanation:

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Step-by-step explanation:

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Samantha claims that 4x + 2 is equivalent to the expression x + 17 + 3x − 15. Check whether Samantha’s equivalent expression is correct using x = 2. Samantha is incorrect because when using x = 2, the resulting values in both expressions are different. Samantha is incorrect because the expressions cannot be checked using x = 2. Samantha is correct because when using x = 2, the resulting values in both expressions are equal.

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Answer:

The correct answer is c

Answer:

Answer is c

Step-by-step explanation:

Your welcome

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Answers

Answer:

= -32a+64b

Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation: Domain is the x coordinates and range is the y coordinates

Solve for x in the equation: 2x-7=14

Answers

Add 7 to both sides
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Step-by-step explanation:

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Answers

Answer:

163

Step-by-step explanation:

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Answer:163

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Answers

Answer:

10 families have cats

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Step-by-step explanation:

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B D and E.

Step-by-step explanation:

The bottom one Staples has 9 cases of crayons with 1452 boxes in each case
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Answers

Answer:

d. 16,092

Step-by-step explanation:

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Answers

Answer:15

Step-by-step explanation:

what are the three products of celullar respiration

Answers

Answer:

Cellular respiration is this process in which oxygen and glucose are used to create ATP, carbon dioxide, and water. ATP, carbon dioxide, and water are all products of this process because they are what is created.

Step-by-step explanation:

Solve for x.
9(x + 1) = 25 + x
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Answers

Answer:

Step-by-step explanation:

9(x+1)=25+x

9x+9=25+x  subtract x both sides

8x+9=25    subtract 9 both sides

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Anna makes unique jewelry. The owner of the "Unique" store agreed with Anna to deliver 20 bracelets a week. At the moment, Anna has 80 bracelets made, and can make 17 bracelets a week. For how many consecutive weeks will Anna be able to supply her bracelets to the "Unique" store?

Answers

Answer:

7 weeks

Step-by-step explanation:

80 ÷ 20 = 4

She over those four week she makes 17 per week. So,

17 × 4 = 68

Next, divide the product by 20:

68 ÷ 20 = 3.4

But 3.4 is only 3 full weeks so then its 3.

Lastly, add the 3 weeks we just solved for the the 4 weeks from before and you get 7 weeks.

So, Anna will be able to supply the "Unique" store for 7 weeks.

I HOPE I HELPED!!!!!!!!!! :))))))

The temperature increases from 18° F to 27° F.
What is the percent increase of the temperature?
A
3%
B
9%
С
33%
D
50%

Answers

Either 50% or 9%
Because it can be both

The percent increase in the temperature is 50%.

To understand more, check below explanation.

Percentage increase:

The temperature increases from 18° F to 27° F.

       Increase in temperature = 27 - 18 = 9

The percent increase in the temperature is computed as,

                                  [tex]=\frac{27-18}{18}*100\\ \\=\frac{9}{18}*100\\ \\=\frac{1}{2}*100=50\%[/tex]

Learn more about the percentage here:

https://brainly.com/question/24304697


(PLEASEEE HELP) Which graph of which line represents a
proportional relationship?
Graph A
Graph B
Graph C
Graph D
Look carefully at the graph of multiple graphs shown below. Which of the graphs
represents or shows a proportional relationship?

Answers

Graph B represents a proportional relationship.

Answer:

B

a proportional relationship in a graph needs to go through the 0.0, and also needs to be a stright line.

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= -x + 6
A
y = -2x + 3
y=-3x +3
y = ;& + 3
Done

Answers

Yes it’s the 2 choice

What is the slope of 3x-2y=7?

Answers

Answer:

The slope is -3/2

Step-by-step explanation:

Hope this helped have a good day!

A rock is thrown from a cliff into a ravine. The function ℎ() = −16^2 + 19 + 2560 describes the height, in feet, of the rock from the ground seconds after it is thrown. What is the height of the rock, in feet, 2 seconds after it is thrown?

Answers

Answer:

d

Step-by-step explanation:

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