(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x = 2. The graph of g(x) is blue.
Let h(x) = f(g(x)). Find
A. h'(1) =
B. h'(2) =
C. h'(3) =

(1 Point) Use The Graph Below To Find Exact Values Of The Indicated Derivatives, Or State That They Do

Answers

Answer 1

Derivatives can be calculated from graphed functions.

The values of the derivatives are:

The given parameter is:

[tex]\mathbf{h(x) = f(g(x))}[/tex]

Start by calculating the equations of f(x) and g(x)

Graph f(x)

The slopes of f(x) are: 3/2 and -3/2

So, the equations are:

[tex]\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}[/tex]

[tex]\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}[/tex]

Graph g(x)

The slope of g(x) is: -1/2

So, the equation is:

[tex]\mathbf{g(x) = -\frac 12x}[/tex]

For x = 1 and x = 2, we have:

So, we have:

[tex]\mathbf{h(x) = f(g(x))}[/tex]

Where:

[tex]\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]

[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes

[tex]\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}[/tex]

Open brackets

[tex]\mathbf{h(x) = -\frac{3}{4}x}[/tex]

Differentiate

[tex]\mathbf{h'(x) = -\frac{3}{4}}[/tex]

So:

[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex]

[tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex]

For x = 3, we have:

[tex]\mathbf{h(x) = f(g(x))}[/tex]

Where:

[tex]\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]

[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes

[tex]\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}[/tex]

[tex]\mathbf{h(x) = \frac{3}{4}x}[/tex]

Differentiate

[tex]\mathbf{h'(x) = \frac{3}{4}}[/tex]

Substitute 3 for x

[tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]

Hence, the values of the derivatives are:

[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex], [tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex] and [tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]

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Related Questions

Please help! Will brainliest!

Answers

Answer:

a= 6-b ,,, a+b=6

a+b= -2a-3,,, 3a+b=-3

2a=-9,,, a= -9/ 2

b= 21/2

Consider the functions p(x) = 5x3 + 6x2 + 4x and qx) = 5640.
-
1. Use graphing technology to find a value of that makes p(x) = q() true.

Answers

In order to make p(x) = q(x) true, x would have to equal 181.935

Graphing technology used in image below

Please help! Not sure what the question is asking exactly and need this last problem done asap!

Answers

Answer:

look at the photo..............

9514 1404 393

Answer:

  log₅(21) = log₅(3) +log₅(7)

Step-by-step explanation:

The relevant relation is ...

  log(ab) = log(a) +log(b)

where the logs have any consistent base.

__

Here, we have ,,,

  ab = 21 = 3·7.

Then ...

  log(21) = log(3) +log(7)

When the logs are to base 5, that becomes ...

  log₅(21) = log₅(3) +log₅(7)

Keith plays basketball at a gym. He can get a $20 membership card and pay $2 for every visit, or he can go any time and just pay $5 for each visit. Which two equations represent the two options for his
number of visits with his total ccost?

Answers

The two equations that can be used to represent his number of visits with his total cost will be 20 + 2x and 5x.

Let the number of visits be represented by x.

Since Keith can get a $20 membership card and pay $2 for every visit, or he can go any time and just pay $5 for each visit, then the equation to represent the information will be:

20 + (2 × x) = (5 × x)

20 + 2x = 5x

Therefore, the equations will be 20 + 2x and 5x.

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pls help
its hw pls help
ill try to make brainiest

Answers

1 = t=8. 2= x=8. 3. M= 7/5. 4. Y= 2/3. The last one might be wrong sorry it’s hard to see.

Answer:

1. 8. 2. 8. 3.  7/5. 4. 2/3.

Step-by-step explanation:

As you can see you just need to cross multiplication and use distirbitive property

Please give brainiest

Help with questions 21-23 using pemdas

If u can, please help with some ones below those (using pemdas) :]

Tyyy

Answers

Answer:

21. 123    22. 6.86 or 6/ 6/7  23. 90

Step-by-step explanation:

21. (6+4)² + (22+10÷2)

     (10)² + (22 + 5)

        100 + 27

           127

22. (11+42-5) ÷ (11-4)

         48 ÷ 7

        6.85 or 6 6/7

23. (17-3) × (14 - 6) -22

         14 × 8 - 22

         112 - 22

           90

Simplify.
- 2x - } – 5x + i + x
-
х
-
17/3
-
3
+
10
х
Enter your answer in the box.
Do not use decimals in your answer.

Answers

Answer:

I'dont think it's 77 or not right

Given info:-

Evaluate:

[(1⅕ - 2/5).(-3/5)³]÷(-9)

⇛[6/5 - 2/5).(3³/5³)]÷(-9)

Take the LCM 5 & 5 is 5.

⇛[(6-2 /5). (3*3*3/5*5*5)]÷(-9)

⇛[(4/5).(27/125)]÷(-9)

⇛[4/5 × 27/125)]÷(-9)

⇛[(4*27)/(5*125)]÷(-9)

⇛[20/625] ÷ (-9)

⇛[20/625] ÷ 1/9

⇛20/625 × 9/1

⇛(20*9)/(625*1)

⇛180/625

Now, reduce the fraction by extracting and cancaling out with 5.

⇛36/125 or 0.228 Ans.

Hope this helps!

1/5×8 simplified =?!?!

Answers

your answer is 8/5 as an improper fraction simplified

Answer:

the answer is 1.6

Step-by-step explanation:

AB= 10.2 cm and Bc= 3.7 cm find the length of AC

Answers

Answer:

3.2333

Step-by-step explanation:

HELP!! Will give brainliest

Answers

Answer:

my brother said it was  

Step-by-step explanation:

1400.053...

what is the present value of $6,000 to be received at the end of 6 years if the discount is 12%

Answers

Future value = FV = $6000

Time period = n = 8

interest rate = r = 12%

Present value (PV) is calculated using the formula:

PV = FV/(1+r)n

Present Value = PV = 6000/(1+12%)8 = 6000/1.128 = 2423.299368

Answer -> 2,423

Answer:

$3,039.79

Step-by-step explanation:

Find the slope of the line passing through the pair of points. (If an answer does not exist, enter DNE.)
(10, 0), (0, −6)

Answers

Answer:

0.6

Step-by-step explanation:

Lets plug these points in:

[tex]\frac{((-6)-0)}{(0-10)} =\frac{-6}{-10} =0.6[/tex]

Help with question 13 only please.

Answers

I think it is B

It makes the most sense to me to do that

Hi, this is multiplication with decimals, help!

Answers

Answer:

Sean paid 0.25 more cents than Cal.

Step-by-step explanation:

Cal's problem: 2.4 * 2.55 = 6.12

Sean's problem: 2.6 * 2.45 = 6.37

Answer:

I think 0.25

Step-by-step explanation:

Multipled 2.4 and 2.55 then multipled 2.6 and 2.45. I got 6.12 and 6.37 Then subtracted them and got 0.25

Maths Question - Topic Pythagoras

Please answer the question. Awarding 20 points

Answers

So for this you use a formula which is

a2 + b2 = c2

You name the highest one c, the rest are you choice

so now it will be - x2 + 7 2 = 14 2

you now square them,

now they will be x2 + 49 = 196

now it will be easy to solve it.

Q1) Gary has 40 oranges. Gary gives Maya 1/4 of his oranges. Gary also loses 2/5 of the rest of them. How many does Gary have left? ​

Answers

Answer: 3

Step-by-step explanation:

To find what 1/4 of 40 is you divide 40 by 4.
40/4 = 10
So, if he gave away 1/4 of his oranges he now has 30 oranges left

Next, to find 2/5 of 30, divide 30 by 5 and multiply by 2
30/5=6
6•2=12
So, he lost 12 oranges which leaves him with 18.

40-10=30
30-12=18

Gary has 18 oranges left

what is 4/5 divided by 2/3 simplest form

Answers

Answer:

6/5

Step-by-step explanation:

4/5 divided by 2/3 in simplest form is 6/5.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

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

Given;

4/5 divided by 2/3

Now,

=(4/5)/(2/3)

=12/10

=6/5

Therefore, by algebra answer in simplest form will be 6/5.

More about the Algebra link is given below.

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#SPJ5

How do I solve 0.0055 m a cm ?

Answers

Answer:

863.83

Step-by-step explanation:

es por qué es un número multimedios y los los número se asen pares

dl

This question has been answered, thank you so much for trying to help ^^

Answers

Ok, but don't spend so much of points it will create a shortages of point for u only, if point will get less then you will not able to ask question anymore.

Got it ^_^

I will ask this question based on the above pic. So I'm picking up a question for this.

Anyways thanks for giving away 26 points to me :))

I'm also asking a question with that amount of points. OK

Please answer will mark BRAINILEST!!

Answers

Answer:

Coordinates A and B: (1, 0) and (3, 0)

Coordinates of P: (0, 3)

Coordinates of Q: (2, -1)

Step-by-step explanation:

You're pretty much given the x-intercepts from the original equation.

y = (x - 1)(x - 3). So to get the x-intercepts (points A and B), y has to equal 0. So,

0 = (x - 1)(x - 3).

and y = 0 when x equals 1 and 3. Because anything multiplied by 0 equals 0. So substituting 1 for the value of x, for example, we get:

0 = (1 - 1)(1 - 3)

0 = 0 * (-2)

So there are your x-intercepts, points A and B.

Now,

Expand the brackets of the equation.

y = (x - 1)(x - 3) becomes

y = x^2  -  4x  + 3

You get the y-intercept (point P) by substituting 0 for the value of x. Doing so gives:

y = 0^2 - 4*0 + 3

y = 0 - 0 + 3

y = 3

So, we have our y-intercept (0, 3).

Point Q, the x-coordinate of the vertex is calculated with the equation -b/2a

Taking our expanded equation: x^2 - 4x + 3

which is of the form ax^2 + bx + c

So we find the values of a, b and c and input the values into the equation

a = 1

b = -4

c = 3

So, inputting these into the vertex equation, gives:

-(-4) / 2 * 1

4 / 2

2

So we have the x-coordinate of the vertex. Now that we know that, we can just substitute it into the expanded equation to give the y-coordinate:

y = 2^2 - 4*2 + 3

y = 4 - 8 + 3

y = -1

So there's our y-coordinate, and now we have both the x and y coordinate for the vertex, point Q. (2, -1).

ABC has side lengths 5 inches, 7 inches, and 10 inches.
JKL has side lengths 12
inches, 35 inches, and 37 inches. PQR has side lengths 13 inches, 10 inches, and 16
inches.

Answers

Answer: Obtuse, Right, Acute

Step-by-step explanation:

ABC: 5²+ 7² = 10²

25 + 49 = 100

c is greater so it is obtuse.

JKL: 12² + 35² = 37²

144 + 1225 = 1369

1369 = 1369

legs are equal to c so it is right.

PQR: 13² + 10² = 16²

169 + 100 + 256

269 = 256

c is less so it is acute.

What percent of the students in
applied majors are majoring in
electronics, industrial design, or civil engineering?

Answers

electronics- 40%
industrial design- 20%
civil engineering- 100%
not sure but best of luck :)

Two trains leave stations 420 miles apart at the same time and travel toward each other. One train travels at 65 miles per hour while the other travels at 85
miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.

Answers

Answer:

2hr 48 minutes

Step-by-step explanation:

65t + 85t = 420

150t = 420

t = 2 120/150 = 2 4/5 = 2hr 48 minutes

Time taken by two trains to cover 420 miles is 2hr 48 minutes.

Given, that two trains are travelling towards each other.

Relation between speed, time and distance:

Distance = Speed × Time

When the two trains are travelling towards each other the speeds of two trains are added.

When the two trains are moving in same direction then the relative speed is difference of the two.

So, here the trains are moving towards each other.

65t + 85t = 420

150t = 420

t = 420/150

t = 42/15

t = 2hr 48 minutes

Therefore total time required by two trains to meet is  2hr 48 minutes.

Know more about speed, time and distance,

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Find the slope between these two points:
(4,7).(-6, -4)

Answers

Answer:

1.1

Step-by-step explanation:

slope = (-4-7)/(-6-4)= -11/-10 = 1.1

Please explain why 31% is the answer

Answers

9514 1404 393

Answer:

  b)  31%

Step-by-step explanation:

95% of the normal distribution is between Z values of ±1.96.

99% of the normal distribution is between Z values of ±2.576.

The change from a 95% interval to a 99% interval widens the range by ...

  (2.576/1.96 -1) × 100% ≈ 31.4%

The width of the interval increases about 31%.

__

Compare the two attachments. The tail area of 0.05 means the central area is 0.95. Similarly, the tail area of 0.01 means the central area is 0.99.

_____

Additional comment

As always, when you're dealing with percentages, you need to understand what the base value is. Here, when we're talking about 95% and 99% confidence intervals, we're not talking about the numbers 0.95 and 0.99 and the increase from 0.95 to 0.99.

Rather we're talking about areas under the normal probability distribution curve, and the Z-values associated with those intervals. The change in interval width refers to the change in Z-values associated with the areas of 0.95 and 0.99.

help please if you can. Thank you

Answers

27/50 is the answer. Why? Because 54 and 100 are both divisible by 2. hope this helps

Answer:

6/11

Step-by-step explanation:

I don't know that's what my mom said

Có 2 chuông gà: chuồng 1 có 5 trống 10 mái ,chuồng 2 có 6 trống 14 mái. Có 1 con ở chuồng 2 nhảy sang chuồng 1 . từ chuồng 1 bắt ngẫu nhiên ra 2 con. Tính xác suất bắt được
a . 2 con trống

Answers

I need English to answer

D
C
Out of every five students at a school,
there are two who take art as an elective.
h
С
If sixty students are taking art, how many
students attend the school?

Answers

Answer:

210

Step-by-step explanation:

210 students attend the school. if 60 students are taking art, and there are 2 art students in every 7 students, that means there are 30 groups of 7 because 30×2=60 so since the other 5 do not take art, you would multiply 30×5 and get 150. Then you would add 60 and you would get 210

Calvina Miller makes a car payment of $214.50 every month. Her car
loan is for 5 years. How much will she pay in 5 years?

Answers

12,870 is the answer

Write an expression for the perimeter of the triangle shown below:
A). 5.5x − 9

B). 5.5x + 9

C). 10x − 39

D). 10x − 9

Answers

Answer:

  Answer B    5.5x + 9

Step-by-step explanation:

Perimeter is the distance around the three sides of the triangle

P = (0.3x + 24) + (5x) + (0.2x - 15)

P = (0.3x + 5x + 0.2x) + (24 - 15)

P = 5.5x + 9

Other Questions
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