Let f be a function having derivatives of all orders for allreal numbers. The third-degree Taylor polynomial for f about x=2 isgiven by
T(x) = 7-9(x-2)2-3(x-2)3
a. find f(2) and f '' (2).
b. Is there enough information given to determine wheather fhas a critical point at x = 2?
If not, explain why not.
If so, determine whether f(2) is a relative maximum, arelative minimum, or neither, and justify your answer.
c. Use T(x) to find an approximation for f(0). Is there enoughinformation given to determine whether f has a critical point atx=0?
If not, explain why not.
If so, determine whether f (0) is a relative maximum, arelative minimum, or neither, and justify your answer.
d. The fourth derivative of f satisfies the inequality for all x in the closed interval [0,2]. Use thelagrange error bound on the approximation to f (0) found in part(c) to explain why f (0) is negative.
Solution :
Given : [tex]$T(x)=7-9(x-2)^2-3(x-2)^3$[/tex]
a). f(2) = T(2) = 7
[tex]$\frac{f""(2)}{2!} =-9$[/tex] , so f''(2) = [tex]$-18$[/tex]
b). Yes, since f'(2) = T'(2) [tex]$=$[/tex] 0, [tex]$f$[/tex] does have the critical point at [tex]$x=2.$[/tex]
Since f''(2) = [tex]$-18$[/tex] < 0, [tex]$f(2)$[/tex] is relative maximum value.
c). [tex]$f(0)=T(0)=-5$[/tex]
It is also not possible for determining if [tex]$f$[/tex] has a critical point at x = 0 because [tex]$T(x)$[/tex] gives exact information only at [tex]$x=2.$[/tex]
d). The Lagrange [tex]$\text{error}$[/tex] bound [tex]$=\frac{6}{4!}|0-2|^4= 4$[/tex]
[tex]$f(0) \leq T(0)+4 = -1$[/tex]
Therefore, [tex]$f(0)$[/tex] is negative.
If a test is worth 90 points and I got 12/15 questions right then what would my grade be?
Answer: 80
Step-by-step explanation:
pllssss help I put B, but I got it wrong the first time. NO LINKS
Answer:
D.1767.1 in³
Step-by-step explanation:
volume of a sphere=4/3πr³
where r=radius of the sphere
Given diemeter= 15in
so radius=15/2=7.5in
volume=4/3×π×(7.5)³
=4/3×22/7×(7.5)³
=1767.1in³
hope it helps...
have a great day!!
whats the answer to this?
Answer:
x=6
Step-by-step explanation:
Please answer this onee :C
Answer:
1
Step-by-step explanation:
Answer:
A) 1
Step-by-step explanation:
The number 1 was spun the fewest times. We know this because there is only one x above the 1, suggesting it wa spun the fewest times.
Hope it helps!!!
a) 5x-12=2x-3
b) 8x+2=5x+8
c) 7x-5=4x-2
please
What's the question?
What are we supposed to do?
If Thomas maintains a rate of 20 miles per hour riding his bicycle in a rally that covers 24 miles, how long will it take him to complete the race?
O 2 hours
O 1.2 hours
O 0.8 hours
O 2.4 hours
Answer:
1h=20m
60/4
0,25min+1h
1+0,25
=1,2
He will complete the race in 1.2 hours time.
Hence, option B is correct.
What is Measurement unit?A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that,
The distance completing in 1 hour = 20 miles
So 1 miles of distance is covered in = 1/20 hours
It is also given that,
The distance of rally = 24 miles.
Therefore,
The time taken to cover 24 miles = 24/20
= 1.2
Thus,
The required time = 1.2 hours
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Given the figure below, find the values of x and z.
Answer:
x = 12
z = 101
Step-by-step explanation:
Hello There!
First lets find z
Well the angle that has a measure of 79 degrees and angle z are supplementary angles meaning that the sum of the two is 180
So we can find the missing angle by subtract the given angle (79 in this case) from 180
180 - 79 = 101 so z = 101
Now lets find x
The angle that has a measure of 79 degrees and the angle labeled (6x+7) are vertical angles
If you didn't know vertical angles are congruent
That being said lets create an equation to solve for x
79 = 6x + 7
now we solve for x
step 1 subtract 7 from each side by
7 - 7 cancels out
79 - 7 = 72
now we have 72 = 6x
step 2 divide each side by 6
72/6=12
6x/6=x
we're left with x = 12
2. find the surface area of 12 in 6 in 6 in Your answer
Answer:
276 in^2
Step-by-step explanation:
2((6*6)/2) + 2(6*12) + (8*12) = 276 in^2
Concession stand sales for each game in season are $320, $540, $230, $450, $280, and $580. What is the mean sales per game? Explain how you got your answer.
Answer:
$400
Step-by-step explanation:
all you do is add 320+540+230+450+280+580/6 and the asnwe comes out to 400
Darius wants to buy a new car. The car he chooses has a total purchase price of $18,500. Darius uses a multi-offer website to apply for a car loan. He receives three offers with minimum payments he can afford. The terms for each loan are shown in the table.
Darius belive he should chose loan option B. Which of the following statements about Darius’s choice is true?
A. Darius should choose loan option B because it has the shortest loan term.
B. Darius should not choose loan option B because he will pay $398.52 more in interest than on loan option C.
C. Darius should choose loan option B because he will pay $280.44 less in interest than on loan option A.
D. Darius should not choose loan option B because it does not have the lowest interest rate.
Answer:
the correct answer is B, Darius should not choose loan option B because he will pay $398.52 more in interest than on loan option C.
Step-by-step explanation:
I also had this question, and it showed that I got it correct :)
What is the volume of this cylinder?
6 m
7 m
Round your answer to the nearest tenth.
Answer:
(Refer below:)
Step-by-step explanation:
Because there is no image, here's what I'm going to assume: there are multiple scenarios. Refer to each one below:
1) Where r = 6 and h = 7:
V = Bh
V = (π r²) (h)
V = (6² π) (7)
V = 36π (7)
V = 252π
2) Where r = 7 and h = 6:
V = Bh
V = (π r²) (h)
V = (7² π) (6)
V = 49π (6)
V = 294π
3) Where d = 6 and h = 7:
d = 2r = 6
r = 3
V = Bh
V = (π r²) (h)
V = (3² π) (7)
V = 9π (7)
V = 63π
4) Where d = 7 and h = 6:
d = 2r = 7
r = 3.5
V = Bh
V = (π r²) (h)
V = (3.5² π) (7)
V = 12.25π (7)
V = 87.75π ≈ 269.39
MSL7
Dificuit Dimensions
A tool box has the dimensions of 8 in by 7 in by 4 in. If Jacob plans to double all three
dimensions to build a larger tool box, he believes he would double the volume of the tool box,
Is he correct?
13=X/4
A. 13/4
B. 4/13
C. 52
D. 9
Answer:
Hi! The answer to your question is C. 52
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!
- Brooklynn Deka
What value does the 2 represent in the number 0.826
Answer:
.02
Step-by-step explanation:
A trapezoid was broken into a rectangle and a triangle. What is the length, b, of the base of the triangle?
O 2 cm
O 4 cm
O 6 cm
O 8 cm
Answer:
2
Step-by-step explanation:
because if 10 is the whole line of the base at the bottom of the trapezoid
and 8 is the whole top 10-8=2
Find the length of the side labeled x. Round intermediate values to the nearest 10th. Use the rounded values to calculate the next value. Round your final answer to the nearest 10th
Answer:
16.0(?)
Step-by-step explanation:
I’m not really sure if it’s correct. But I’m assume it’s correct.
Solve: |2x − 1| < 11.
Express the solution in set-builder notation.
{x|5 < x < 6}
{x|–5 < x < 6}
{x|x < 6}
{x|–6 < x < 6}
Answer:
the second one is the answer
Step-by-step explanation:
hope that helps
Answer:
B; {x|–5 < x < 6}
Step-by-step explanation:
Find the missing side of this right triangle 8 13
Answer: x = √105
Step-by-step explanation:
a² + b² = c²
8² + x² = 13²
64 + x² = 169
x² = 105
x = √105
What is the surface area of this prism?
5 yd
5 yd
11 yd
6 yd
If 5.90 × 1.8 = 10.62, what does 106.2 ÷ 59 equal?
Answer:
1.8
Step-by-step explanation:
- hope this helps!!
please HELP! USE PYTHAGOREAN THEOREM TO FIND RIGHT TRIANGLE SIDE LENGTHS
formula A(2)+B(2)=C(2)
Answer:
x = √ 40
Step-by-step explanation:
6 x 6 = 36 2 x 2 = 4 36 + 4 = 40Help me please it’s due today
The drawing shows a semicircular window separated into 3 sections of colored glass
Approximately how many square inches of the tinted glass are red
Answer:
141.3
Step-by-step explanation:
27.78% of the total area is covered with red.
What is the area of a sector? What is a expression? What is a mathematical equation?A part of a circle is called sector. The area of a sector is given by -(Ф/360) x πr²
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the given semicircle as shown in image.
Total green coloured area -
A[G] = 2 x {(Ф/360) x πr²}
A[G] = 2 x (40/360 x πr²}
A[G] = (2/9)πr²
Now -
A[R] = πr²/2 - (2/9)πr²
A[R] = πr²{1/2 - 2/9}
A[R]% = (πr²{1/2 - 2/9}/πr²) x 100
A[R]% = (1/2 - 2/9) x 100
A[R]% = (9 - 4)/18 x 100
A[R]% = 5/18 x 100
A[R]% = 500/18
A[R]% = 27.78%
Therefore, 27.78% of the total area is covered with red.
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can someone dooo ittttttttt
Answer:
i dont know
Step-by-step explanation:
Which solution for z makes the equation true?? 10+10+z=40=10 (pls explain why. Thanks)
Answer:
z=30
Step-by-step explanation:
40-10=30
10+10+?=30
30-10-10=10
I'm sorry cuz I don't know how to explain it
Answer:
z = 10
Step-by-step explanation:
10 + 10 + z = 40 - 10
10 + 10 + z = 30
10 + 10 + 10 = 30
since 40 - 10 = 30, then Z has to equal 10 because 10 + 10 + z needs to be 30
Simplify 7 - 2(5 - 2x)
Answer:
4 − 3
Step-by-step explanation:
Which expression is Equivalent to is m<4?
Answer:
first option
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ 4 is an exterior angle of the triangle, then
∠ 4 = ∠ 2 + ∠ 3
A square dance floor has a perimeter of 120 yards.
What is the length of a diagonal of the dance floor?
O 38.3 yd
O 30 yd
O 60 yd
O 42.4 yd
Which of the following is a correct interpretation of the expression -4- (-7)?
Choose 1 answer:
The number that is
to the left of -7 on the number line
B
The number that is 4 to the right of -7 on the number line
The number that is 7 to the left of -4 on the number line
D
The number that is 7 to the right of -4 on the number line
Answer:
I think option (d) is right answer
Answer:
c
Step-by-step explanation: