(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) =
Answers
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
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
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).
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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HELP!! Will give brainliest
Answers
Answer:
my brother said it was
Step-by-step explanation:
1400.053...
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
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 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)
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
Graphing technology used in image below
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
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
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
Help with question 13 only please.
Answers
I think it is B
It makes the most sense to me to do that
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:
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
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.
What percent of the students in
applied majors are majoring in
electronics, industrial design, or civil engineering?
Answers
industrial design- 20%
civil engineering- 100%
not sure but best of luck :)
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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help please if you can. Thank you
Answers
Answer:
6/11
Step-by-step explanation:
I don't know that's what my mom said
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]
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.
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
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
1/5×8 simplified =?!?!
Answers
Answer:
the answer is 1.6
Step-by-step explanation:
pls help
its hw pls help
ill try to make brainiest
Answers
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
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!
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
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.
AB= 10.2 cm and Bc= 3.7 cm find the length of AC
Answers
Answer:
3.2333
Step-by-step explanation:
what is the present value of $6,000 to be received at the end of 6 years if the discount is 12%
Answers
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:
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.
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