(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
Which choice is the correct graph of [x1 < 5?
A 4
B
C
D
E
-
F
5
A. Graph A
O B. Graph B
C. Graph
ОО ОООО
O D. Graph D
O E. Graph E
OF. Graph F
Answers
Answer:
B
Step-by-step explanation:
Da"B"a"B"y
2 B so
"B" graph "B"
↑that explains it
In which quadrant does the point (3 , 19) lie?
A.
Quadrant I
B.
Quadrant II
C.
Quadrant IV
D.
Quadrant III
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Answer:
A.
Quadrant I
Step-by-step explanation:
Quadrant I= Both co=ordinates positive.
please help
with this question
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Answer:
its
Step-by-step explanation:
A is what my brother said
lim┬(x→1)〖(1-√x)/(x^2-1)〗
Answers
Answer:
- 1/4
Step-by-step explanation:
[tex]\frac{1-\sqrt{x} }{x^{2}-1 } = \frac{(1-\sqrt{x})*(1+\sqrt{x} ) }{(x+1)(x-1)(1+\sqrt{x} )} \\= \frac{1-x}{-(1-x)(x+1)(1+\sqrt{x} )} \\= - \frac{1}{(x+1)(1+\sqrt{x} )} \\ \lim_{->1} - \frac{1}{(x+1)(1+\sqrt{x} )} \\ = -\frac{1}{(1+1)(1+\sqrt{1}) } = - 1/4[/tex]
A manufacturing process is designed to produce bolts with a 0.75-inch diameter. Once each day, a random sample of 36 bolts is selected and the bolt diameters recorded. If the resulting sample mean is less than 0.730 inches or greater than 0.770 inches, the process is shut down for adjustment. The standard deviation for diameter is 0.04 inches. What is the probability that the manufacturing line will be shut down unnecessarily
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0.0028 = 0.28% probability that the manufacturing line will be shut down unnecessarily.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n have standard deviation given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 0.75 inches, thus [tex]\mu = 0.75[/tex].Standard deviation of 0.04 inches, thus [tex]\sigma = 0.04[/tex]Sample of 36, thus [tex]n = 36, s = \frac{0.04}{\sqrt{36}} = 0.0067[/tex].The probability of being shutdown is the probability of a sample mean less than 0.73 inches or more than 0.77 inches. They are the same distance to the mean(0.02), thus, considering the Central Limit Theorem:
[tex]z = \frac{0.02}{s}[/tex]
[tex]z = \frac{0.02}{0.0067}[/tex]
[tex]z = 2.99[/tex]
The probability is P(|z| > 2.99), which is 2 multiplied by the p-value of z = -2.99.
z = -2.99 has a p-value of 0.0014.
2(0.0014) = 0.0028
0.0028 = 0.28% probability that the manufacturing line will be shut down unnecessarily.
A similar problem is given at https://brainly.com/question/25212662
1. The value of angle A is
50°. What is the value of
angle B?
Answers
Answer:
130º
Step-by-step explanation:
a line is 180º so if one angle is 50 then it's just 180-50
Click on the least amount of rainfall.
Answers
The least amount is the smallest amount, 1/8.
A normal conversation is about 10^7 times the threshold of hearing. Compute the intensity level (in decibels) for a normal conversation.
Answers
Answer:
70
Step-by-step explanation:
The sound of a normal conversation 3 is times intense than the sound of a computer.
What is sound intensity?It is the energy flow per unit area. It refers to the product of pressure and velocity of particles in a fluid medium, which is equivalent to the power received per unit area.
Let us say the sound intensity of the quietest noise a person can hear is 60 decibels. So the sound intensity of computer is 20 decibels.
Sound intensity of a normal conversation/ computer sound, will be:
[tex]SI=\frac{60}{20} =3[/tex]
Therefore, the sound of a normal conversation 3 is times intense than the sound of a computer.
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1. A new drill is used to dig a hole in the ground. At noon, the hole is 13.2 feet deep when the new drill is turned on for the first time that day. At 2 p.m., the drill has dug the hole to be feet deep. The new drill dug 1.5 times as much of the hole as the old drill would have in the same length of time.
(a) What expression represents the number of feet the new drill dug?
(b) How many feet would the old drill have dug in the same length of time? Show your work. Answer the question in a complete sentence.
Answers
Using the subtraction and division operation, the depth dug by the new drill, and the depth that would have been dug by the old drill are 29.05 feets and 19.37 feets respectively.
The expression for the number of feets dug by the new drill can be calculated thus :
Final depth - Initial depthDepth dug = 42.25 feets - 13.2 feets
Depth dug = 29.05 feets
The new drill dug 1.5 times the depth that woukd have been dug by the old drill :
Depth dug by old drill = 29.05 / 1.5
Depth dug by old drill = 19.37 feets
Therefore, the depth dug by old drill will be 19.37 feets
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Help please for brainliest
Answers
Answer:
C
Step-by-step explanation:
a quadratic polynomial has an x² term
a binomial has 2 terms
leading coefficient is the coefficient of the term with largest exponent
4x² - 8x
is a quadratic (x² term )
is a binomial ( has 2 terms )
has a leading coefficient of 4 (4x² )
Keisha and Jen went out to eat for dinner their meal together were $45.76 they want to leave a 20% tip how much total
Answers
Answer:
I'm only guessing its $25.76 but just to classify you should probably ask
en la feria del condado, la calabaza con la cinta roja pesaba 108 libras menos que la calabaza con la cinta azul. cuanto pesaba la calabaza con la cinta azul?
Answers
Answer:
sorry i dont know
Step-by-step explanation:
In the 2004 Summer Olympics, Adam van Koeverden of Oakville, Ontario, won two medals. He won the gold medal in the men’s 500 m kayak race, with a time of 1 min 37.9 s. He also won the bronze medal in the 1000 m race, with a time of 3 min 28.2 s. In which race did he row with greater speed?
Answers
Answer:
Adam van Koeverden at the 2004 Olympic at Athens. Van Koeverden paddled to victory in the Men's K1 500 m kayaking event, adding a gold medal to the bronze he won days earlier in the 1000 m to become Canada's first double medallist in the summer Olympics since Donovan Bailey and Clara Hughes at Atlanta in 1996.
Step-by-step explanation:
Pls mark me as brainliest
Helpp i have 12 minutes
Answers
Answer:
the answer is 924.8 round it up and you get 925
Step-by-step explanation:
A theme park has a Ferris wheel that takes 2 minutes to go around its 450-foot circumference. The equation · (130) = 450 relates the speed of the Ferris wheel to its circumference. What exactly does represent?
Answers
Answer: The Ferris wheel’s speed in feet per hour.
Step-by-step explanation:
complete the following sentence by using Cooperative adjective
Answers
Answer:
m
Step-by-step explanation:
Solve for x: 34= -2
x= ????
Answers
Answer:
You haven't typed the equation correctly
x=-17
Step-by-step explanation:
Which kind of triangle is showing
Answers
Answer:
it's an scalene triangle
having all the sides and angels different from each other
Step-by-step explanation:
brainliest plz
What’s the LCM of 9 and 6
Answers
Answer:18
Step-by-step explanation:
6 : 6,12,18
9: 9,18
Hi there!
»»————- ★ ————-««
I believe your answer is:
LCM (9,6): 18
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\text{Multiples of 6: }6,12,\textbf{18},24\\\\\text{Multiples of 9: } 9,\textbf{18}, 27, 36\\\\\\\text{Since 18 is the first common multiple that appears, it is the LCM.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
pls help
which trend line properly describes the data relationship in the scatterplot?
Answers
Answer:
The 2nd one
Step-by-step explanation:
The trend line properly describes the data relationship in the scatterplot is plot A.
What is Trend line?A trend line is also known as a line of best fit, and it is used to illustrate the behaviour of a set of data to assess if it is in a given pattern. So, a trend line is an analytical technique that is frequently used in conjunction with a scatter plot to determine whether or not there is a relationship between two variables.
As, per the plots.
The scatter plot A have the points distributed symmetrically on the both side of line.
Also, straights lines are negatively correlated with scatter points.
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Does (5, 4) make the equation y = –7x true? Yes Or No
Answers
Answer:
No
Step-by-step explanation:
Given point ,
(5,4)Substitute ,
y = -7x 4 = -7*5 4 = -35 ( Not true )Answer:
No
Step-by-step explanation:
Substitute the x- coordinate into the equation and if the value equals the y- coordinate then it makes the equation true.
y = - 7(5) = - 35 ≠ 4
Thus (5, 4 ) does not make the equation true
What is the coefficient in the expression - X + 21?
Answers
Answer:
there are no like terms
Step-by-step explanation:
-x + 21 = -x + 21
A coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable next to it.
The negative sign right next to x represents the coefficient of -1. It's the same thing as -1 • x + 21.
Please helppppppppppppp!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
558
Step-by-step explanation:
The sum of the first n numbers is ½n(n + 1)
which is the left most number in each row number n
so finding the row containing 526
½n(n + 1) > 526
½n² + ½n > 526
n² + n > 1052
n² + n - 1052 > 0
n > (-1 + √(1² - 4(1)(-1052))) / 2(1)
n > 31.938
so 526 is almost to the end of the 32 row.
The end of that row is ½(32(33)) = 528
so 526 resides two spaces to the right of 528
The end of the row below it, row 33, is ½(33)(34) = 561
As each row is one number longer than the previous row, we count back
2 + 1 = 3 numbers from the end to find what is under 526
561 - 3 = 558
PLEASE HELP ITS MATH THANK YOUUUU
Answers
Answer:
it is 9 centimeters
Step-by-step explanation:
it is a 1:1 ratio
so 9 kilometers would be 900000 centimeters
IF YOU ARE REALLY GOOD A MATH THEN PLEASE ANSWER THIS !!!
Your help will be much appreciated because i am losing my sanity doing this math
Answers
c-9
to find the amount of parents in the room we'd have take away the amoutn if children in the room from the total amount of people
25-9
thus, your expression to represent the amount of parents would be
c-9
Hope this helped you- have a good day bro cya)
Hey everyone I would greatly appreciate some help here :)
I’m doing a chapter quiz and I honestly am 99% sure this is right but since it’s a big quiz I thought it wouldn’t be bad to get a second opinion and if I’m wrong a step by step answer so I can do it properly next time ok so here is question
Jasmine opened a bank account and she deposited 84.50 dollars into her account every month for 20 months. She also used 50.50 every month to pay for dance lessons, after 20 months she used 1/49& the total money left in her account to go to camp. What is the total amount of money jasmine spent to go to the camp?
115
135
155 or
170
Now I picked 170 because I got 680 from all that and 1/4 of 680 is 170 atleast I’m 99% sure lol if I’m right just let me know but if I’m wrong please tell me how so I can do it properly next time :)
Answers
Answer:15
Step-by-step explanation:
On a piece of paper, graph y-3 > 2x + 2. Then determine which answer
choice matches the graph you drew.
A
B
с
D
56(0.5
56(0.5)
56(0,5)
5°(0,5
-5 (-3,-1)
5
-5 (-3,-1)
5
5 (-3,-1)
5
6 (-3,-1)
5
-5
A. Graph A
B. Graph B
c. Graph C
D. Graph D
Answers
9514 1404 393
Answer:
C. Graph C
Step-by-step explanation:
All of the graphs show the boundary line with the correct slope and y-intercept. To figure which graph, you can ignore everything except "y" and the inequality symbol. That means we're looking at ...
y >
So, the values of y that are solutions are greater than those on the boundary line. The values on the boundary line are not included. This means the shading of the solution area is above the dashed boundary line, as shown in Graph C.
What is the unit cost per bottle if a pack of 12 bottles of juice sells for $6? (1 point)
$0.50 per bottle
$0.72 per bottle
$5.00 per bottle
$7.20 per bottle
Answers
Step-by-step explanation:
12 bottles = $6
1 bottle = 6/12
= $0.50 per bottle.
Hope it helps :)
What is the slope of the line through (-9,-6) and (3,-9)
Answers
Answer:
-1/4
Step-by-step explanation:
y2 - y1 / x2 - x1
-9 - (-6) / 3 - (-9)
-3/12
= -1/4
A card is drawn randomly from a standard deck of 52 cards. Find the probability of the given event. a red 3
Answers
Answer:
1/13
Step-by-step explanation:
Total number of cards = 52
no.of sample space n(s) = 26
no.of favourable cases n(E) = 2
probability of getting red 3 p(E)= n(E) / n(s)
or, 2 /26
or, 1/13