Can someone pls help me find the second derivative of this. I need to find the concave up and down intervals but I’m having trouble getting the second derivative
Answers
Starting from
[tex]f(x)=\dfrac14(x+1)^{\frac83}-4(x+1)^{\frac23}[/tex]
take the first derivative using the power and chain rules:
[tex]f'(x)=\dfrac83\cdot\dfrac14(x+1)^{\frac83-1}-\dfrac23\cdot4(x+1)^{\frac23-1}[/tex]
[tex]f'(x)=\dfrac23(x+1)^{\frac53}-\dfrac83(x+1)^{-\frac13}[/tex]
Now take the second derivative:
[tex]f''(x)=\dfrac53\cdot\dfrac23(x+1)^{\frac53-1}-\left(-\dfrac13\right)\cdot\dfrac83(x+1)^{-\frac13-1}[/tex]
[tex]f''(x)=\boxed{\dfrac{10}9(x+1)^{\frac23}+\dfrac89(x+1)^{-\frac43}}[/tex]
Optionally, you can condense the second derivative a bit by factoring out [tex]\frac89(x+1)^{-\frac43}[/tex], which gives
[tex]f''(x)=\dfrac89 (x+1)^{-\frac43} \left(80(x+1)^{\frac63}+1\right)[/tex]
[tex]f''(x)=\dfrac89 (x+1)^{-\frac43} \left(80(x+1)^2+1\right)[/tex]
[tex]f''(x)=\dfrac89 (x+1)^{-\frac43} \left(80x^2+160x+81\right)[/tex]
Related Questions
The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls. Jalen's Mobile Phone Cost Number of minutes, X 150 220 250 275 x Cost, y $7.50 $11.00 $12.50 $13.75 If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation? O y = 0.05% O y = 20x O y = 157.58 O y = 1125x Save and Exit Net Submit Mark this and return
Answers
Answer: y=0.5x
Step-by-step explanation: hope this would be helpful ∵∵∵∵∵∵∵∵∴∴∴∴∴∴∴∴∴
Solve the real-world situation by using the substitution method.
One smartphone plan costs $30 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone plan costs $60 per month for talk and messaging and $3 per gigabyte of data used each month. Let c represent the total cost in dollars and d represent the amount of data used in gigabytes. The system of equations lbrace c = 30 + 8d c = 60 + 3d can be used to represent this situation.
How many gigabytes would have to be used for the plans to cost the same? What would that cost be?
Both plans would cost $_____
if _____ gigabytes of data are used.
Answers
C=30+8d Data usage here would be 9= and the program would cost $102
C=60+3d. Data usage here would be14=and this program would cost $102
Could I get help with this?
Answers
Answer:
x int= -4 y int= 1
Step-by-step explanation:
intercepts refer to the place on the each axis where the line passes through
You earn 30% commissions on the sales of your new app. If you earn $600 in commissions, what were your total sales?
Answers
Answer:
600.3
Step-by-step explanation:
600.3
The total sale was $2000.
What is percentage?Percentages are fractions that are counted out of 100. The number is followed by this symbol: %. A percentage of an object is how many parts of it there are out of 100 equal parts
Given that, You earn 30% commissions on the sales of your new app, you earn $600 in commissions,
Let the total sales be x,
Therefore, according to the question,
30% of x = 600
x × 30/100 = 600
x = 600 × 100/30
x = 2000
Hence, the total sale was $2000.
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Only need a answer for problem a
Answers
The answer is 120. Find the supplementary angles by subtracting 60 from 180.
180-60=120
X = 120 degrees
The linear pair is angle B and angle C.
Find the simple interest on a loan of 23,000 at 5.4% interest for 11 months
Answers
Answer:
Simple interest=1138.5
Step-by-step explanation:
Simple interest=23000×(5.4/100)×(11/12)
S.I=23000×0.054×(11/12)
S.I=1138.5
I'm not understanding
Answers
Answer:
D. x = 3
Step-by-step explanation:
We would like to find out for what value of x does f(x) = g(x). This is essentially the same as asking us to find the x-value for which f(x) = k, where k is some number, and g(x) = k, as well.
Looking at the two tables provided, we notice that when x = 3, both f(x) and g(x) equal -2. So, the answer is D.
WILL GIVE BRAINLIEST!!
What is the value of 1/60?
Answers
Answer:
1/6
Step-by-step explanation:
Answer:
C. 1
Step-by-step explanation:
18:
A line has a slope of -4 and includes the points (-10,10) and (-7,k). What is the
value for k?
k=
19:
the point (3,4) lies on the graph of the equation 3y=ax+7, then the value of a is
Note: Use slash (/) to separate the numerator and denominator.
200:
Consider a sequence whose first five terms are: -1.75,-0.5,0.75,2,3.25
Which function (with domain all integers n21) could be used to define and continue this
sequence?
A f(n)=7/4(n-1)-5/4
B f(n)=5/4(n-1)-7/4
C f(n)=(7/4)n-5/4
D f(n)=(5/4)n-7/4
Need help with 18-20 plz help I put a picture there to I really need these ASAP
Answers
19- a = 5/3
Determine the equation of the line passing through the point below having the corresponding
slope.
Point: ( - 25, -9)
Slope: m=1/5
Write your answer as an equation in the form
y = mx + b
Answers
Answer:
y=1/5x-4
Step-by-step explanation:
So, first we're gonna put this into point slope form, (y-y1)=m(x-x1), then we'll convert it. When you plug the numbers in, you get (y+9)=1/5(x+25)
Then, you simplify!
y= 1/5(x+25)-9
y=1/5x+5-9
y=1/5x-4
Hope this helped!
which equation is equivalent to y= Ax + By = C
Answers
Answer:
slope intercept form
Step-by-step explanation:
that's what ax + by = c is
xoxo, your highness...Order the following from Least to Greatest: 0, -4 1/4, -1/2, 1, -3 3/5, 2, -4.1, -0.6, 23/5, 6, -1, 4.5, -5, 2.1
Answers
Answer:
-5, -4 1/4, -4.1, -3 3/5, -1, -0.6, 0, 1, 2, 2.1, 4.5
Step-by-step explanation:
1. Find the value of n
(show your work)
n + 7.5 = 48
MUST SHOW WORK!!!
Answers
Answer:
40.5
Step-by-step explanation:
48 - 4.5 = 40.5
40.5 + 7.5 = 48
BRAINLIEST PLEASE
Answer:
40.5
Step-by-step explanation:
48-7.5 (48-7=41-0.5=40.5 so there for that would be your answer :D)
Answer- 40.5
yes the person was correct but here is a understanding ! :D
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION I NEED TO TURN IT IN TODAY
Answers
Answer:
The answer is 833.65384615385
Step-by-step explanation:
pleaseee help
A job placement agency helps match job seekers with potential employers. The agency would like to design a simulation in order to help predict the likely job placement outcomes for job seekers based on historical trends and patterns. Which of the following is most likely to be a benefit of the simulation?
A. The computer simulation will be able to include more details and complexity than the real-world job placement process.
B. The computer simulation could be used to test hypotheses about patterns in the job placement process that are costly or time consuming to observe in reality.
C. The computer simulation will be able to precisely predict the real-world outcomes for each job seeker.
D. The computer simulation will remove the bias that may arise in the real-world job placement process.
Answers
Answer:
B.
Step-by-step explanation:
All computer simulations are designed to test a large number of different scenarios with various sets of data in order to understand each output that certain data generates and ultimately find the best solution. This is the overall main reason why simulations are created. The same applies in this scenario, this simulation will be used to test hypotheses about patterns in the job placement process that are costly or time-consuming to observe in reality. If such tests had to be conducted by actual people it would take months, years, or even decades to generate and analyze all the data.
Answer:
Its D
Step-by-step explanation:
You gotta believe me
Which of these is the simplest form of x2-2x/x2-4?
Answers
Answer:
The first one
Step-by-step explanation: hope this helps!
An above-ground garden is in the shape of a rectangular prism measuring 5 feet by 8 feet by 1.5 feet. The organic soil costs $1.20 per cubic foot. How much will it cost to fill the above-ground garden fully?
Answers
Answer:$72.00
Step-by-step explanation: To find the volume you do 5×8×1.5 which equals 60. Then you multiply 60 by 1.20 to find your total cost. Answer is 72
Write the explicit rule for the arithmetic sequence
-10, -3, 4, 11,...
Answers
a
0
=
4
a
i
=
a
i
−
1
+
7
XXXX
possibly with the restriction 1<=i<=4 if this is not intended to be a continuous sequence
Explanation:
This is a simple arithmetic sequence with a difference of
7
between ascending sequence terms.
6plus 6 times 1 divide 9
Answers
Answer:
6+6x1/9= 6.66666666667
Thats the long way and i used mental math and quick math to get the answer :)
HAVE A WONDERFUL DAY
-ary
Answer:
6.666...
Step-by-step explanation:
6 + 6 * 1 / 9
6 + 6 / 9
6 + 2/3
6.666....
Game Pitches Seen
1 25
2 20
3 20
4 17
5 15
6 14
The table lists the number of pitches seen by a player in 6 games. What is the mean of the data set?
A.
11
B.
14.5
C.
18.5
D.
20
Answers
Answer:
C. 18.5
Step-by-step explanation:
all you have to do is add all the numbers together. Your equation should be 25+20+20+17+15+14 to get the answer of 111. After this all you have to do is divide 111 by how many games were played which is 6. 111÷6 is 18.5
Answer:
a
Step-by-step explanation:
Click the photo to find the measures of the interior angles (3 answers required)
Answers
Answer:
the correct answer is:
68 + x + ( x-24) =180
x + (x-24) = 112
2x - 24 = 112
2x = 112 + 24
2x = 136
x = 68
so ...for another : 68 - 24 = 44
Two printers working together can complete a job in 6 hours. Working alone, one
printer takes three times as long as the other printer. How many hours would each
printer need to complete the job alone?
Answers
Answer:
Press A takes 10 hours to do a certain job. So Press A does (1/10)th of the job in an hour.
Press A and Press B, together do (1/2.5) or (4/10)th of the job in an hour.
So Press B does (4/10)-(1/10) = (3/10)th of the job in an hour. So Press B can do the job in (10/3) hours or 3 hour and 20 mins.
Check: A does (1/10)th and B does (3/10)th part of the job in an hour. A and B together will take (1/10)+(3/10) = 4/10th of the job in an hour. So they will complete the job in 10/4 = 2.5 hours. Correct.
Answer: Press B can do the job in 3 hour and 20 mins.
Step-by-step explanation:
Write an equation for the graph, where y depends on x.
Answers
Answer:
y = -3x + 6
Step-by-step explanation:
Equation of straight line is given by,
y = mx + b
m = slope of the line
b = y-intercept
From the graph attached,
m = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{-6}{2}[/tex]
= -3
y intercept 'b' = 6
Therefore, equation of the line will be,
y = -3x + 6
xander takes a quiz worth 50 points. each question is worth 10 points. sketch a graph to show his score if he missed 1,2,3,4 or 5 questions
Answers
Hope that helps!
I need the steps. Please help me. Thanks!
Answers
Answer:35x^3 + 15x^2 + 42xz + 28x + 18z + 12
Step-by-step explanation:
(7x + 3) (5x^2 + 6z + 4)
7 (5^2 + 6 + 4) +3 (5^2 + 6 + 4)
35^3 +42 + 28 + 15^2 + 18 + 12
35^3 + 15x^2 + 42xz + 28x + 18z + 12
HELP!!!!!A school is having a competition to see who can read the most books in one month (30 days). In the first 5 days, Jake reads 4 books. Meanwhile, Amy reads 5 books over 6 days. If they continue at these rates, who will win? By how many books?
Answers
is there a rate because im not understanding
Lisa is a hairdresser. A cut and color is $85. If her customer gives her a 15% tip on the total cost, how much of a tip would Lisa get?
Answers
Answer:
$12.75 I think
Step-by-step explanation:
Answer:
Lisa got a total tip of $12.75.
Step-by-step explanation:
To answer this question, we just need to find 15% if $85.
85 x 0.15 = 12.75
This means, Lisa got a total tip of $12.75.
Hope this helps! :D
Calc I Question help
Answers
The way the question is phrased, it sounds like the height stays fixed at 18 in. If L and W denote the raft's length and width, respectively, then its volume V is given by
V = 18 L W
Differentiating both sides with respect to time t gives
dV/dt = (18 in) W dL/dt + (18 in) L dW/dt
We're told that dL/dt = -1 in/s and dW/dt = -2 in/s, so that at the moment L = 11 in and W = 4 in, the volume is changing at a rate of
dV/dt = (18 in) (4 in) (-1 in/s) + (18 in) (11 in) (-2 in/s)
dV/dt = -468 in³/s
so the raft is losing air at a rate of 468 in³/s. (Note that "losing" captures the negative sign from before.)
Which inequality has the solution shown in the graph?
a – 3 ≤ –5
a – 3 –2
Answers
Answer:
-2
Step-by-step explanation:
Trust me
A pond contains 110 fish, of which 20 are carp. If 10 fish are caught from the lake, what are the mean and variance of the number of carp among those 10?
Answers
Answer:
Mean = 1.82
Variance = 1.365
Step-by-step explanation:
We define X as the random variable that counts the number of the carp fishes that has been caught. Also we assume that all the fishes are equally likely to be caught. In that case we have that X as hypergeometric distribution.
The of the Hypergeometric Distribution and Its variance is given below.
Mean of the distribution = [tex]n*\frac{k}{N}[/tex]
Variance = [tex]\frac{n*k*(N-k)(N-n)}{N^2(N-1)}[/tex]
N= 110
k = 20
n = 10
Upon calculation we get
Mean = [tex]10*\frac{20}{110}[/tex]
= 1.82
Variance = [tex]\frac{10*20*(110-20)(110-10)}{110*110*(110-1)}[/tex] = 2*90*100/11*11*109 = 1.365
Therefore the mean is 1.82 and variance is 1.365
The mean and the variance of the number of carp are 20/11 and 180/121, respectively
The given parameters are:
Fishes = 110
Carp = 20
The probability of selecting a carp is:
p = 20/110
Simplify
p = 2/11
In a selection of 10 fishes, we have:
n = 10
The mean is:
E(x) = np
This gives
E(x) = 10 * 2/11
E(x) = 20/11
The variance is
Var(x) = E(x) * (1 - p)
So, we have:
Var(x) = 20/11 * (1 - 2/11)
Simplify
Var(x) = 20/11 * 9/11
Evaluate the product
Var(x) = 180/121
Hence, the mean and the variance of the number of carp are 20/11 and 180/121, respectively
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