This is for AP CALCULUS. I really need help on this. I’m trying to find the first and second derivative of these three functions.

This Is For AP CALCULUS. I Really Need Help On This. Im Trying To Find The First And Second Derivative

Answers

Answer 1

Review Material:

[tex]\sqrt[n]{x^m} = x^{\frac{m}{n}}[/tex]

[tex]\frac{d}{dx}[x^n]=nx^{n-1}\\[/tex]

[tex]\frac{d}{dx}[\sin(x)]=\cos(x)\\[/tex]

 [tex]\frac{d}{dx}[\cos(x)]=-\sin(x)\\[/tex]

[tex]\frac{d}{dx}[constant]=0\\[/tex]

Step-by-step explanation:

(a)

[tex]F(x) = -2\cos(x) +x^{\frac{4}{3}} -3e\\ \text{Note: 3e is a constant}\\F'(x) = 2\sin(x) + \frac{4}{3}x^{\frac{1}{3}}\\F''(x) = 2\cos(x) + \frac{4}{9}x^{-\frac{2}{3}}[/tex]

(b)

[tex]F(x) = x^{-3} + \frac{1}{2}x^2-\sin(x)\\F'(x)=-3x^{-4} + x - \cos(x)\\F''(x) = 12x^{-5} + 1 + \sin(x)[/tex]

(c)

[tex]F(x) = 2x^{-3}+x^{\frac{3}{4}}-4x\\F'(x) = -6x^{-4} + \frac{3}{4}x^{-\frac{1}{4}}-4\\F''(x)= 24x^{-5} - \frac{3}{16}x^{-\frac{5}{4}}[/tex]


Related Questions

a bicyclist rides 25 miles every 2 hours during race which equation represents the relationship between the number of miles and the number of hours of the bicyclist rides? let x represent the number of hours and let y represent the number of miles?

Answers

Answer:

y=12.5x

Step-by-step explanation:

How do I solve this!! Quick and urgent (23. Is the number for the equation)

Answers

Answer:

Independent: Time

Dependent: Views

Step-by-step explanation:

Independent variables are the things that are purposefully altered.

Dependent variables are the things that change in response to the independent variables being changed.

As the hours increase, so do the views. The views will change as time goes by. A change in the number of views does not affect the time passed. Therefore, time is the independent variable and the number of views is the dependent variable.

URGENT!! VERY HARD QUESTION. WHAT IS 2+2?? NEED ANSWER RIGHT NOW!!

Answers

Answer:

4

Step-by-step explanation:

2+2=4

This makes zero sense give answer

Answers

Answer:

IQR for males: 3

IQR for females: 2

Q1 for males: 5

Q1 for females: 6

the number of females who spend over 6 hours exercising is greater(?) than the number of males who spent 6 hours exercising

Step-by-step explanation:

An equal amount of men and women were randomly selected and asked how many hours per week they spend excercising

How to find IQR?

to find IQR you have to identify your median(middle value) of the lower and upper half of the data. These are called quartile 1(Q1) and quartile 3(Q3). You subtract these two (Q3 and Q1) and the IQR is the difference.

Males box plot:

Minimum: 1

Maximum: 10

Q1: 5

Q2: 7

Q3: 8

Subtract Q3 and Q1

8 - 5 = 3

This is the IQR

Females box plot:

Minimum: 4

Maximum: 10

Q1: 6

Q2: 7

Q3: 8

Subtract Q3 and Q1

8 - 6 = 2

IQR =2

the number of females who spend over 6 hours exercising is greater than the number of males who spent 6 hours exercising

What is the slope of the line segment?
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15
12
9
6
3
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1 2 3 4 5
0-3
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3
0 1
3
3

Answers

This question is so ez. It 22

Find the area of the rhombus

Answers

[tex]60cm^{2}[/tex]

Step-by-step explanation:

A=pq/2

shorter diagonal= 8cm

longer diagonal = 15cm

15*8 = 120

120/2 = 60

A = [tex]60cm^{2}[/tex]

find the value of x
50°
6
X
Not drawn to scale

Answers

Answer:

Hence option C is correct...hope this helps you:)

Find the value of x in the parallelogram below.

Answers

Answer:

102

Step-by-step explanation:

78 and x are adjacent angles.

Sum of adjacent angles is 180 in a parallelogram.

78 + x = 180

x = 180 - 78

x = 102

Answer:

102°

Step-by-step explanation:

A parallelogram is a special type of quadrilateral that has both the pair of opposite sides parallel and equal.

78+x= 180( adjacent angles in a parallelogram)

x=180-78=102°

The area of a circle is 60.12cm find the length of the radius rounded to 2 dp.

Answers

Answer:

Before you write the answer to your question, make sure the question is asking for the actual value of pi or 3.14.

If the question was asking for the question to be completed with the ACTUAL VALUE of pi, then your answer is ----> 4.37

If the question was asking for the question to be completed with the rounded of pi (3.14), then your answer is ----> 4.38

It's a subtle difference, but remember, there is no such thing as close in math, it's either right or wrong.

Step-by-step explanation:

Given: Circle's Area, 60.12

As the value of pi was not directly stated, I will divide the answer into 2 portions, portion one with the answer with the actual infinite value of pi, and one where I will describe how to do it with 3.14 as pi.

Explanation with 3.14:

First thing first, know the formula for calculating the area of a circle:

[tex]A = \pi r^2[/tex]

[tex]A[/tex] stands for Area, and [tex]r[/tex] stands for Radius

Now, plug in the given values:

[tex]60.12 = \pi r^2[/tex]

Next, replace 3.14 for pi:

[tex]60.12 = (3.14)r^2[/tex]

Then, divide both sides by 3.14 ,which gives us:

[tex]19.15 = r^2[/tex]

Please note: 19.15 is rounded

Anyway, to isolate [tex]r[/tex], we take the square root of both sides:

[tex]\sqrt{19.15} = \sqrt{x^2}[/tex]

The square root and square on the right side of the equation cancel out, and we are left with:

[tex]4.38 = r[/tex]

Please note that 4.38 was rounded

this is an escape room i can't escape

Answers

Answer:

The area of the rectangle is 180 units

Step-by-step explanation:

6 + 2 + 2 = 10

But the areas of each sectioned off shape are

Big rectangle = 180

Small rectangle = 48

2 by 8 triangles = each 8

3 by 8 triangles = each 12

Altogether, it's 268

Answer:

268 square yards

Step-by-step explanation:

small L rectangle   8 x 6 =48

two L triangles   2    * 1/2 * 2 * 8 = 16

Large rectangle 18 x 10 = 180

two R triangles    2    * 1/2 3 x 8 =24    Total = 268 yds^2

One container of lemonade mix weighs 2.33 kilograms. How much will 7 containers weigh?

Answers

Answer:

16.31 kg.

Step-by-step explanation:

2.33 * 7

Natalia makes $17.82 per hour, and is expecting to receive a 10% increase in pay. What can Natalia expect her future hourly rate to be?

Answers

help is on the way! :D

Im sorry if im wrong but i could do 17.82x10= 178.20

If a right circular cylinder and oblique cylinder both have a height of 12 inches and diameter of 6 inches, do they have the same volume? (Use straight pi equals 3.14)
Group of answer choices

Yes, they both have a volume of 339.12 inches cubed.

No, the right circular cylinder has a volume of 339.12 inches cubed and the oblique cylinder has a volume of 1 comma 356.48 inches cubed.

No, the right circular cylinder has a volume of 1 comma 356.48 inches cubedand the oblique cylinder has a volume of 339.12 inches cubed.

Yes, they both have a volume of 1 comma 356.48 inches cubed.

Answers

Answer:

Yes, they both have a volume of 339.12 inches cubed.

Step-by-step explanation:

To calculate the volume of an oblique cylinder is very simple, we must multiply π (Pi = ~ 3.14) by the radius to the power of two and then multiply by the height. In this case the height forms a 90 degree angle from the opposite base to the position of the base, but outside of it.

Volume = π × Radius² × Height

The formula for the volume of a regular cylinder or an oblique cylinder is the same, if we imagine a stack of poker chips (forming a cylinder), even when we tilt the chips to one side (forming an oblique cylinder) the volume remains the same.

Now using this information, we must find the volumes of both cylinders.

For the oblique cylinder:
Given

Radius is 3 (Radius is have the diameter which is 6)Height is 12

Using the formula,

The volume would be 339.29 m³

Now solving for the other cylinder:

V=πr²h=π·32·12≈339.29201

Rounded, the answer would be 33.29 m³

This therefore proves that they both have the same volume.

what is the measurement of angle B

Answers

Answer:

41 degrees

Step-by-step explanation:

All of the angles must add up to 360 degrees to form a circle. So we have 22 + b + 297 = 360. Solving for b, we get b = 41.

6
7
2
5
The usual price of a TV set was $400. During Memorial Day weekend, the price was marked down to
$335. What was the percent decrease in the price of the TV set?
сл

Answers

Answer:

The answer is 65% is the percent decrease

The measures of the angles of a triangle are shown in the figure below solve for X

Answers

Answer:

29 degrees

Step-by-step explanation:

The interior angles of all triangles equals 180. We know already that we have 101 and 50 degrees. If we add that, we get 151. To find x, we have to simply subtract 151 from 180. If we do this, we get 29. x=29.

Hope this helps!

Given the points K(-2;5), L(1,3) and M(-5; 2p). Calculate the value
of p if KL ILM.

How do I solve this question?

Answers

The product of the perpendicular lines is a negative one. Then the value of p will be negative 3.75.

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Given the points K(-2,5), L(1,3) and M(-5, 2p).

If KL is perpendicular to LM. Then we have

The slope of KL will be

KL = (1+2)/(3-5)

KL = -1.5

The slope of LM will be

LM = (1+6)/(3-2p)

LM = 7/(3-2p)

We know the product of the perpendicular lines is a negative one.

        KL x ML = -1

-1.5 x 7/(3-2p) = -1

              -10.5 = -3 + 2p

                 2p = -7.5

                   p = -3.75

More about the coordinate geometry link is given below.

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It's going 2 by 2 for the paper i couldn't get it all in at a time so the first 2 are one paper and its like that for the next 2 papers but the last paper is the whole paper

Answers

it took I'd :safalbista10 10

Indigo needs to order some new supplies for the restaurant where she works. The restaurant needs at least 430 knives. There are currently 269 knives. If each set on sale contains 18 knives, what is the minimum number of sets of knives Indigo should buy?

Answers

The minimum number of sets of knives Indigo should buy is 9.

What is Inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Here, Let the minimum number of sets be x.  

          restaurant needs at least 430 knives

         currently restaurant have 269 knives

         each set contains 18 knives.

According to question,

           18x + 269 ≥ 430

            18x ≥ 161

              x ≥ 161/18

              x ≥ 8.94

Thus, the minimum number of sets of knives Indigo should buy is 9.

Learn more about Inequality from:

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Consider the following shape. Find the value of x. Round your answer to two decimal places.

Answers

Answer: 7.81

Step-by-step explanation:

The volume of a cylinder is 4πx3 cubic units and its height is x units.


Which expression represents the radius of the cylinder, in units?

: 2x, 4x

Answers

Expression represents the radius of the cylinder, 2x units.

What is a cylinder?

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

Given that:

Volume of cylinder =[tex]4\pi x^{3}[/tex]

we know that, Volume of cylinder = [tex]\pi r^{2} h[/tex]

[tex]4\pi x^{3}[/tex]= π * [tex]r^{2}[/tex] *h

[tex]4x^{3} = r^{2}*h[/tex]

[tex]4x^{3} = r^{2}*x[/tex]      [since, height=x]

[tex]4x^{2} = r^{2}[/tex]

r= 2x

Hence the radius of the cylinder is 2x units

Learn more cylinder here:

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what can Tiffany conclude from the data above?​

Answers

A person who has only a high school diploma, they are most likely to have an income of less than $40,000.

What is probability?

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

The probability of a high school diploma person having less than $40,000 income will be

P(HSD) = 51/78

P(HSD) = 0.6538

The probability of a Bachelor's degree person having less than $40,000 income will be

P(BD) = 24/78

P(BD) = 0.3077

The probability of a master's degree person having less than $40,000 income will be

P(MD) = 3/78

P(MD) = 0.0385

A person who has only a high school diploma, they are most likely to have an income of less than $40,000.

More about the probability link is given below.

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Question: Write an equation for this.

You have total 100 coins
that consist of 50 cents
and 10 cents. The total
money is 34 dollar. Find the
number of the 50 cent
coin.

Answers

To solve this question, we need to write out an equation for this and proceed to solve the system of equation. the number of 50 cents coins are 60.

System of Equation

The given data in this problem are

number of coins = 10050 cents = x10 cents = yamount = $34

The system of equations can be written as

[tex]x + y= 100...eq(i)\\0.5x + 0.1y = $34..eq(ii)[/tex]

Let's start with equation (i)

[tex]x + y = 100\\\\y = 100 - x[/tex]

Substitute equation (iii) into equation (ii)

[tex]0.5x + 0.1(100 - x) = 34\\0.5x + 10 - 0.1x = 34\\0.4x = 24\\x = 60[/tex]

From the calculations above, the number of 50 cents coins are 60.

Learn more on system of equations here;

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Find the sum of 2/3 and it’s additive inverse

Answers

Answer:

0

Step-by-step explanation:

2/3 additive inverse is 2/3

-2/3+2/3 is neutral = zero

-2/3+2/3 = 0

Find the missing side

Answers

Answer:

5^2+7^2= 12^2 so your answer should be 12

X=-3
A. 64
B. 8
C. 4
D. 16

Answers

Answer:

The answer is A.

Step-by-step explanation:

I took the test

Find the area of triangle​

Answers

Answer:

C- 17 cm

A- 9cm

Step-by-step explanation:

C - because plus 9 and 8 is 17 cm

A - because plus 4 and 5 is 9 cm

What is the image point df (-2, -3) after a translation right 2 units and up 4 units?

Answers

Answer:

(0, 1)

Step-by-step explanation:

right 2 units: add 2 to x

up 4 units: add 4 to y

Answer: (0, 1)

A municipal trash facility allows a person to throw away a maximum of 40 pounds of trash per week. Last week, 195 people threw away the maximum allowable trash. How many tons of trash did this equal

Answers

The total tons of trash that was thrown away by the people is 3.9 tons.

How many tons of thrash was thrown away?

The first step is to convert pounds to tons

1 pound  = 0.0005 tons

40 x 0.0005 = 0.02 tons

The second step is to multiply 0.02 by 195

0.02 x 195 = 3.9 tons

To learn more about multiplication, please check: https://brainly.com/question/13814687

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emergency!!

Write the function f(x)=x² – 25x in the form f(x) = a(x - h)? +k. Identify the vertex.


Answers

Answer:

See below

Step-by-step explanation:

Complete the square

[tex]f(x)=x^2-25x\\\\f(x)+(\frac{-25}{2})^2=x^2-25x+(\frac{-25}{2})^2\\\\f(x)+156.25=x^2-25x+156.25\\\\f(x)+156.25=(x-12.5)^2\\\\f(x)=(x-12.5)^2-156.25\\\\f(x)=(x-\frac{25}{2})^2-\frac{625}{156}[/tex]

Identify vertex

[tex](h,k)\rightarrow(-\frac{25}{2},-\frac{625}{156})[/tex]

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