No, the function f(x) = x^3 - 3x + 7 is continuous and differentiable on the closed interval [-2, 2], so it satisfies the hypotheses of the Mean Value Theorem.
To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to find the average rate of change of f on the interval [-2, 2], which is:
f(2) - f(-2) / 2 - (-2) = (2^3 - 3(2) + 7) - ((-2)^3 - 3(-2) + 7) / 4
Simplifying, we get:
f(2) - f(-2) / 4 = (8 - 6 + 7) - (-8 + 6 + 7) / 4 = 19/2
So, there exists at least one number c in the open interval (-2, 2) such that f'(c) = 19/2. To find this number, we take the derivative of f(x):
f'(x) = 3x^2 - 3
Setting f'(c) = 19/2, we get:
3c^2 - 3 = 19/2
3c^2 = 25/2
c^2 = 25/6
No, the function f(x) = x^3 - 3x + 7 is continuous and differentiable on the closed interval [-2, 2], so it satisfies the hypotheses of the Mean Value Theorem.
To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to find the average rate of change of f on the interval [-2, 2], which is:
f(2) - f(-2) / 2 - (-2) = (2^3 - 3(2) + 7) - ((-2)^3 - 3(-2) + 7) / 4
Simplifying, we get:
f(2) - f(-2) / 4 = (8 - 6 + 7) - (-8 + 6 + 7) / 4 = 19/2
So, there exists at least one number c in the open interval (-2, 2) such that f'(c) = 19/2. To find this number, we take the derivative of f(x):
f'(x) = 3x^2 - 3
Setting f'(c) = 19/2, we get:
3c^2 - 3 = 19/2
3c^2 = 25/2
c^2 = 25/6
c = ±sqrt(25/6)
So, the numbers that satisfy the conclusion of the Mean Value Theorem are c = sqrt(25/6) and c = -sqrt(25/6), or approximately c = ±1.29.
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Which expression represents the factor form of the equation above ?
Answer:
(x+4)(x+25)
Step-by-step explanation:
x*x=x^2
x*20=20x
4*x=4x
4*25=100
x^2+20x+4x+100
put the commons together and you will get
x^2+29x+100
jake has a recipe that uses 4 cups of flour. He has a bag with 48 cups of flour. He wants to know how many recipes he can make using the bag of
flour. He finds the answer using this number sentence:
48 4=
Which number sentence shows another way to solve this problem?
A x 4 = 48
B. 48 x = 4
C 0 : 4 = 48
D. 4: 48 = 0
Answer:
D
Step-by-step explanation:
It is just like 4/48.
Answer: b
Step-by-step explanation: b because you can multiply which 48 times 4
what is the ratio then what is the value of the ration?
Answer:
For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3).
What's the circumference of a circle with a radius of 5 inches
Answer:
10π
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
Find the product of 2x4(3x2 + 4x + 1).
6X6 + 8x5 + 2x4
6x3 + 3x4+1
5X6 + 6x5 + 3x4
5x8 + 6x4 + 1
Answer:
A: 6X6 + 8x5 + 2x4
Step-by-step explanation:
A bag has some purple marbles and
some green marbles in it. This can be
modeled with the following equation.
T = p + g.
Solve the equation for the number of
purple marbles, p.
Enter the variable that belongs in the green box.
p = [?] - [ ]
Answer:
p= T-g
Step-by-step explanation:
Answer:
p=t-g
Step-by-step explanation:
if sin theta = cos theta,theta is an acute angle then tan theta=?
please answer within one hour
I will mark u brainliest
Answer:
hope it helped have a good day mate
Can someone please help me ASAP
Answer:
Look down below!
Step-by-step explanation:
Fist, make your inequality:
-x + 5y > -10
5y > x - 10
y = .2x - 2
Now, plug in any value of x to find y!
Ex: x = 5...
y = .2 (5) - 2
y = -1
Your first coordinate could be (5, -1)
Hope this helps!
On a loan of $4,500 for 2 1/2 years at 4% per year, how much do you wind up paying to pay off the loan?
Answer:
4,950
Step-by-step explanation:
4,500*.10=450
4,500+450=4,950
Hope this helps:)
Help please and tysm
6 x (5 + 4) - 3 - (2+1)
A 18
B) 30
C) 48
D) 54
Answer:
54
Step-by-step explanation:
need to know the middle part
[tex]\Large\boxed{\tt Answer:~3x=2x+10;~x=10}[/tex]
[tex]\tt Step-by-step~explanation:[/tex]
Since it shows us that both ends of the segment in the middle bisects the sides of the triangle in the middle, we know that the segment in the middle is half of the hypotenuse (4x + 20).
[tex]\tt a)~ 3x =\frac{1}{2} (4x+20)[/tex]
Let's solve the right side of the equation by distributing[tex]\tt 0.5 (4x+20)\\4x*0.5=2x\\20*0.5=10\\\\b)~2x+10;~3x=2x+10[/tex]
Now, we can solve for x by moving the variable x to one side of the equation and everything else on the other side.
[tex]\tt 3x-(2x)=2x-(2x)+10\\\\c)~x=10[/tex]
Solve for x and y.
8
5
Х
15
У
12
Answer:
1.84553470835e+37
Step-by-step explanation:
Mr. Mika paid a total of $150 to rent a room at a hotel for two nights. The table shows information about four other
guests who rented rooms at the hotel.
Hotel Bills
Number of Nights
Room Was Rented
Total Amount
Paid
Guest
1
6
$450
II
3
$225
III
8
$600
IV
5
$360
Which guest did NOT pay the same nightly rate that Mr. Mika did?
Answer:
Well, one night at the hotel equals $75.
Step-by-step explanation:
All you have to do is mulitlpy the nights by $75.
The last one is wrong it should be
5 nights = $375.
Hope this helps! Bye
Need help ASAP 25 points
Answer:
The volume is 24 cubic cenimeters. Can i be brainlyest? Lol i know i spelled it wrong :l
Step-by-step explanation:
Slope of 4,-9 and 8,-3
Answer:
3+5=8 its question answer ok
Answer:
slope=. y2-y1/x2-x1
= -3+9/8-4
= 6/4
=3/2
Determine if the triangles are congruent by HL, SAS, SSS, AAS, or
ASA
Somebody help please!!!
A sailboat with a sick passenger abroad is following a parabolic path given by the equation = − 2 +2 + 8.
The boat’s captain sent out a distress signal. A speedboat is trying to catch the sailboat to provide medical aid and is on a path given by the linear equation y=- x+8. Besides the y-intercept (starting location) where do the paths of the two boats cross (for each graph you must plot at least 3 points each and give answer in coordinate pair notation)?
A sailboat with a sick passenger aboard is following a parabolic path given by the equation y=-2x+8. T...
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George wants to buy a new television that is on sale for 1/4 off the regular price of $599.96. The sales tax is 7%. What is the final price of the television including tax?
Answer:
641.96
Step-by-step explanation:
Write an solve the inequality. A gym charges a one time sign-up fee of $10.25 and then $5 each time you go. A student can pay up to $135.25. How many times can the student go to the gym?
Answer:
25 visits
Step-by-step explanation:
Given data
One time fee= $10.25
let the number of times visited be x
and the total cost for x visits be y
Hence
y=10.25+5x------------1
for y=135.25
let us find x
135.25= 10.25+5x
135.25-10.25= 5x
125=5x
x= 125/5
[tex]x\geq 25 visits[/tex]
1/4 y + 9=1/2 A -34 b 2 c 9 d 38
find the value of -
[tex]( {x}^{2} - x)[/tex]
where, x = 5
Step-by-step explanation:
(x^2 -x)=(5^2-5)
=25-5 =20
Answer:
(x²-x)=(5²-5)
=(25-5)
=(20)ans..............
A rectangle has a length of 2y inches and a width of y - 4 inches. If the perimeter of the rectangle is 22 inches, what is y? What is the length? What is the width?
PLS SHOW HOW YOU SOLVED THE PROBLEM
15. The perimeter of an isosceles triangle is 34 inches. When you add the base of the
triangle to one of the equal sides the sum is 18. What is the length of the base of the
triangle?
a)
2 inches
go to card 3
b) 14 inches
go to card 6
c) 9 inches
go to card 9
d) 16 inches
go to card 11
e) 4 inches
go to card 13
Answer:
D
Step-by-step explanation:
ayo!! listen to me this is an easy question :)
Apples are on sale at the local fruit stand at 4 lbs. for $2.60. Which equation can be used to find the cost, c, of n pounds of apples?
c = 4
c = .65n
c = 2.60n
c = 8n
Answer:
B ) c = 0.65n
Step-by-step explanation:
To find how much a single pound costs, divide the total cost by the total weight (2.60 ÷ 4). So, the cost (c), equals $0.65 per pound.
Find the square root. 1/16
Answer:
The square root of 1/16 is 1/4=0.25
Step-by-step explanation:
The square root of 1/16 is 1/4.
To find the square root of 1/16, you can take the square root of the numerator and the denominator separately.
√(1/16) = √1 / √16
Since the square root of 1 is 1, and the square root of 16 is 4:
√(1/16) = 1/4
So, the square root of 1/16 is 1/4.
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3x-4y=-14 6x+3y=27 don’t understand how to solve
tama Ang kanyang sagot
the length and breadth of a hall are 20m and 15m respectively. find the area of 4 Walls of the hall if the height of the hall is 10 m
Answer: 700m^2
Step-by-step explanation:
length = 20m
breadth= 15m
so we use lateral surface area = 2(L+B) H
area of hall = 2(20+15)10
2×35×10 = 700m^2 ans
Find the point-slope equation for the line that passes through the points (-6, 24) and (5, -31). Use the first point in your equation. y - [?] = [ ](x-[ ])
if the slop of the straight line passing through the two points A (4, k) , B (3, 2) is 5, find the value of K
Answer:
Step-by-step explanation:
*The dashes are the fraction line*
To find slope...
difference between y
-------------------------------
difference between x
2 - k
------- = 5
3 - 4
3-4 = -1 so...
-1 ( 2 - k ) = 5
k - 2 = 5
k = 7
Hope this helps!
Answer:
2.5 or 5/2
Step-by-step explanation:
Y2-Y1/X2-X1=m
(2-k)/(3-4)=5
(2-k)/-1=5
Multiply both sides by -1
(2-k)/2=-2.5
-k/-1=-2.5/-1
k=2.5 or 5/2
A savings account earns 7% interest each year, compounded quarterly (4 times a year). If a person invests $300 and makes no further deposits or withdrawals, what is the balance in the account after 5 years
Answer:
.
Step-by-step explanation: