Answers
Work Shown:
f(x) = 4x^(-2) + (1/4)x^2 + 4
f ' (x) = 4*(-2)x^(-3) + (1/4)*2x .... power rule
f ' (x) = -8x^(-3) + (1/2)x
f ' (2) = -8(2)^(-3) + (1/2)*(2)
f ' (2) = 0
Finding the derivative, we have that f'(2) = 0, option D.
-----------------------------
The derivative of an exponent is:[tex](x^n)^{\prime} = nx^{n-1}[/tex]
Additionally, the sum of the derivatives is the derivative of the sum. The derivative of a constant is zero.-----------------------------
The function is:
[tex]f(x) = 4x^{-2} + \frac{x^2}{4} + 4[/tex]
The derivatives are:
[tex](4x^{-2})^{\prime} = -2 \times 4x^{-2 -1} = -8x^{-3}[/tex]
[tex](\frac{x^2}{4})^{\prime} = \frac{2x}{4}[/tex]
[tex](4)^{\prime} = 0[/tex]
Thus, the derivative of the function is:
[tex]f^{\prime}(x) = -8x^{-3} + \frac{2x}{4} = -\frac{8}{x^3} + \frac{2x}{4}[/tex]
At x = 2:
[tex]f^{\prime}(2) = -\frac{8}{2^3} + \frac{2(2)}{4} = -1 + 1 = 0[/tex]
Thus f'(2) = 0, option D.
A similar problem is given at https://brainly.com/question/10037173
Related Questions
Which of the following is the complete list of roots for the polynomial function f (x) = (x squared + 6 x + 8) (x squared + 6 x + 13)?
Answers
[tex]( {x}^{2} + 6x + 8)( {x}^{2} + 6x + 13) =0 \\ [/tex]
_________________________________
[tex] {x}^{2} + 6x + 8 = 0 [/tex]
[tex](x + 2)(x + 4) = 0[/tex]
##############################
[tex]x + 2 = 0[/tex]
[tex]x = - 2[/tex]
##############################
[tex]x + 4 = 0[/tex]
[tex]x = - 4[/tex]
_________________________________
[tex] {x}^{2} + 6x + 13 = 0 [/tex]
[tex]∆ = {b}^{2} - 4ac [/tex]
[tex]a = coefficient \: \: of \: \: {x}^{2} = 1 [/tex]
[tex]b = coefficient \: \: of \: \: x = 6[/tex]
[tex]c = the \: \: alone \: \: number \: = 13 \\ [/tex]
Thus ;
[tex]∆ = ({6})^{2} - 4 \times (2) \times (13) [/tex]
[tex]∆ = 36 - 104[/tex]
[tex]∆ = - 68[/tex]
=======================================
Point :
Remember from now on ,
In quadratic functions ;
if :
[tex]∆ > 0[/tex]
The function has two roots
if :
[tex]∆ = 0[/tex]
The function has just one root
if :
[tex]∆ < 0[/tex]
The function doesn't have any root.
=======================================
Thus , ( x² + 6x + 13 ) doesn't have any root.
So ; ( x = - 2 ) & ( x = - 4 ) are the only roots.
_________________________________
And we're done....♥️♥️♥️♥️♥️
Answer:
c)-2,-4,-3+2i,-3-2i
Step-by-step explanation:
edge2020
I really need help please.Write the equation of the line that passes through the points (-4,2) and (-7,-7) show all your work below
Answers
Answer:
y=3x+14
Step-by-step explanation:
Calculate the slope from 2 points.
Substitute either point into the equation.
Solve for b, which is the y-intercept of the line.
Substitute b, -1, into the equation from step 2.
hope it helps
Five pounds is equal to 2.268 kilograms. How many kilograms is 2 pounds?
Please hurry
Answers
Answer:
2 pounds = 0.9072 kilograms
Step-by-step explanation:
Answer:
it is b
Step-by-step explanation:
What is the solution for the equation?
a+ 8/3= 2/3
Answers
Answer:
a=-2
Step-by-step explanation:
Round 56,650,243 to the nearest ten million
Answers
Answer:
57,000,000
Step-by-step explanation:
57,000,000
Explanation:
fill in the blank to make the equation have infinite solutions
0.01(450x+900)=___x+9
Answers
Hope to help you.have a good day!
PLEASE HELP! Mr. Jones is renovating his backyard, which includes extending his patio. The design drawn by his landscaper use a scale of 1 inch=3.5 feet. If the patio is 5 inches long on the diagram and the orginal patio is 9 feet long, by how many feet is he extending it?
Answers
Answer:
8.5 ft I believe
Step-by-step explanation:
1 in=3.5 ft, so 5in=5(3.5)= 17.5 ft
17.5-9=8.5 ft
If a translation is described as (x -5, y), how has the original image changed?
Answers
Answer:
It moves the x value 5 units to the left.
Step-by-step explanation:
"x - 5" means that we are subtracting 5 to whatever x value we are given. The "y" value doesn't change.
Since we are subtracting to the x value, we are going to move left 5 units.
Let's say we had the point (5, 5).
If we use the translation rule;
(5 - 5, 5)
(0, 5)
We moved the x value 5 units to the left.
Best of Luck!
What is the inverse of the function y - 2 = 3x?
Answers
Answer:
I think the answer is y=[tex]\frac{x-2}{3}[/tex]
Step-by-step explanation:
The tables show the numbers of white and yellow flowers Cara and Hector used in 5 different arrangements.
Cara's Flower Arrangements
White
6 9 12
Yellow 5 10
20
3
15
15
25
White
Hector's Flower Arrangements
4
8 12 16
6 10 14 18
20
Yellow
22
Part A
Are the numbers of white and yellow flowers in Cara's arrangements proportional?
Which equation relates the number of white flowers, w, to the number of yellow flowers, y?
А.
В.
C. No: y = 3 + 5w
D. No: y = 5+ 3w
00.00
Part B
Are the numbers of white and yellow flowers in Hector's arrangements proportional?
Write an equation to relate the number of white flowers, h, to the number of yellow flowers, e.
A
Yes, e
Answers
Answer:
Part A - Yes; y=5/3w Part B - No; e=h+2
Step-by-step explanation:
The tables show the numbers of white and yellow flowers Cara and Hector used in 5 different arrangements.
Cara’s Flower Arrangements Proportional
White 3 6 9 12 15
Yellow 5 10 15 20 25
Hector’s Flower Arrangements Not Proportional
White 4 8 12 16 20
Yellow 6 10 14 18 22
Part A
Are the numbers of white and yellow flowers in Cara’s arrangements proportional?
Which equation relates the number of white flowers, w, to the number of yellow flowers, y?
Yes; y=3/5w
Yes; y=5/3w CORRECT ANSWER
No; y=3w+5w
No; y=5+3w
Part B
Are the numbers of white and yellow flowers in Hector’s arrangements proportional?
Which equation relates the number of white flowers, h, to the number of yellow flowers, e?
Yes; e=3/2h
Yes; e=2/3h
No; e=h+2 CORRECT ANSWER
No; e=h−2
They are correct because Part A is 1.666667 thats more than 1 so it cant be the first, and Part B, its the White flowers plus 2 to be Yellow flowers, not -.
Following are the solution to the given question:
Using the proportionate connection theory to model these two tables, we may conclude the first table is proportionate whereas the second is not.Clara's configuration:[tex]\bold{White (w) }\\\\\bold{Yellow (y)}[/tex]
To determine whether a relationship is proportionate, perform the following tests:[tex]\bold{y = kw } \\\\\bold{5 = 3k}[/tex]
Yes, there seems to be a proportional relationship. Hector's set-up is as follows:[tex]\bold{White (h) }\\\\\bold{Yellow (e)}\\\\[/tex]
The number of yellow flowers always out-numbers the number of white blooms by a factor of 2. As a result, the relationship could be modeled as follows;[tex]\to \bold{e = h + 2}[/tex]
As a result, the relationship is not proportionate.Learn more:
brainly.com/question/18297651
Rakim charges $2 per hour for tutoring plus a $7 fee.
Joan charges a $3 fee plus $4 per hour.
When will their tutoring fees be the same (aka equal)
How many hours of tutoring will occur before the fees are the same?
How much has each person been paid in tutoring fees?
Answers
Answer:
after 2 hours, they will have the same fee.
they will have been payed 11$
Step-by-step explanation:
if you say h = hours of tutoring,
Rakim charges 7 + 2h
Joan charges 3 + 4h
since you want them to be the same, you can write the following equation:
7 + 2h = 3 + 4h
subtract 2h from each side
7 = 3 + 2h
subtract 3 from each side
4 = 2h
divide both sides by 2.
h = 2
after 2 hours, they will have the same fee.
they will have been payed 11$
"they will have been payed" ah yes the grammar.
Bruno uses a piece of wrapping paper with dimensions 1 and one-fourth feet by 3 feet to wrap a gift. What is the total area of the paper used to wrap the gift?
Answers
Answer:
Its 3 3/4 or D
Step-by-step explanation:
Just in case you didn’t understand answer above
is 19 and 95 co-prime
Answers
Answer:
No
Step-by-step explanation:
19 is a prime number but 95 is not.
95= 1x95
5x19
Step-by-step explanation:
19 is a prime number. Factors of 19 up to 100 are 19, 38, 57, 76, 95. ... Thus, there are 95 co-prime numbers to 19 exists between 1 and 100.
can someone pls help with this brainliest gets answer
Answers
Answer:
1. True; 10, 20, 50, 100, 1210 are all divisible by 10.
2. True; prime numbers: 2, 3, 5, 7, 11, 13. Only 2 is even.
3. False; 144 is a perfect square and has 15 factors.
4. False; x = 9 in this equation, so x = 4 is false.
6x-4 and 6(x-4) *
A: Yes, they are equivalent
B: No, they're not equivalent
Answers
Answer:
yes they are equivalent
HELPPPP!!! pleaseeeeee Describe the transformation of F(x)=x2 represented by g
Answers
Answer:g(x)=x-2+2
Step-by-step explanation:
Kid
On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is . How long will it take the airplane to travel 800 miles? Do not include units (hours) in your answer.
Answers
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question
On a flight New York to London an airplane travels at a constant speed. An equation relating the distance traveled in miles d to the number of hours flying t is t= 1/500d. How long will it take the airplane to travel 800 miles?
Speed is the change in distance if a body with respect to time. It is expressed mathematically according to the question as t = 1/500 × d
To determine the time it will take to travel 800miles, we will substitute d = 800 into the modeled equation.
t = 1/500 × 800
t = 800/500
t = 8/5
t = 1.6
2 MULTIPLE CHOICE EASY!! In July, Ariel recorded the height of a pine tree and how quickly it was expected to grow in the next several months.
1. 14$ or 12$ ??
2. $4.50 or $5.50
3.
Y= 4.5X + 22
or
Y= 4.5X +12
Answers
Answer:
3
Step-by-step explanation:!!
Suppose that under your health insurance policy, hospital expenses are subject to a $750 deductible and $150 per day copay. You get sick and are hospitalized for 4 days, and the bill (after your insurance discounts are applied) comes to $6,250. How much of that hospital bill will you have to pay yourself?
Answers
Answer:
$4900
Step-by-step explanation:
It is given that,
According to health insurance policy, hospital expenses are subject to a $750 deductible and $150 per day copay.
If a person hospitalized for 4 days, it would mean that charges will be ($150 × 4 = $600 per day).
Total amount given by insurance policy = $750 + $600 = $1350
The bill for 4 days come out to be $6,250.
The person have to pay ($6,250-$1350) = $4900 itself.
What is the coefficient of
the term of degree 6 in the
polynomial below?
3x^2 – 14x^6 + 6x^3 + 12x +
5x^5
Answers
Answer:
14
Step-by-step explanation:
The coefficient is the number before the degree. In this equation, it looks to be that the number before the 6th degree is 14.
Do these pairs of values (x and y) represent two quantities that are
proportional?
A. Yes, because as x increases, y increases.
B. No, because not all of the pairs represent the same ratio.
C. Yes, because the ratios į and i are equal.
O D. No, because not all of the pairs are simplified ratios.
Answers
Answer: B) No, because not all of the pairs represent the same ratio
For each row, divide y over x
Row 1: y/x = 5/3 = 1.67 approximately
Row 2: y/x = 7.4 = 1.75
Row 3: y/x = 10/6 = 1.67 approximately
Row 4: y/x = 15/9 = 1.67 approximately
We see that row 2 has a ratio different from the others. If we were able to ignore this row, then the answer would be "yes x and y are proportional". However, we cannot ignore this row so that's why the answer is choice B.
We want to see if the relationship between x and y is proportional or not.
We will see that the correct option is B:
"No, because not all of the pairs represent the same ratio."
Let's see how to solve this.
First, a proportional relationship is something of the form:
y = k*x
Where k is the constant of proportionality.
So to see if the relationship between x and y is proportional, we can input the pairs on the general proportional relationship.
For the first pair, we have x = 3 and y = 5, then:
5 = k*3
Now we can find the value of k:
k = 5/3 = 1.667
Now let's do the same for the second pair of points, we should get the same constant of proportionality.
7 = k*4
k = 7/4 = 1.75
So we got different constants of proportionality for two different x-y pairs, thus, the relationship is not proportional.
Because k is defined as the ratio between y and x, we can say that the relationship is not proportional because not all of the pairs represent the same ratio.
Thus the correct option is B.
If you want to learn more, you can read:
https://brainly.com/question/13114933
a = 6, b = 3 and c = 2:
2(a + b) – c = ______
Answers
Answer: 16
Step-by-step explanation:
2(6+3)-2
12+6-2
18-2
16
find angle b show your work
Answers
Answer:
42°
Step-by-step explanation:
The angle measure of 295° just means we are working with a circle.
A circle totals to 360°.
If we add what we are given; 295 + 23 = 318°
We have the total angle measure we are given and "b" which we need to solve.
We can subtract 360 by what we are given to find angle "b"
360 - 318 = 42°
Best of Luck!
Evaluate the expression when a = 6, b = 3 and c = 2:
2(a + b) – c = ______?
Answers
Answer:
16
Step-by-step explanation:
2(6+3)-2 = 2(9)-2 = 18-2 = 16
the equations above define w and z in terms of a. What is 2wz in terms of a?
w=a+2
z=a
Answers
Work Shown:
2wz = 2*(w)*(z)
2wz = 2*(a+2)*(z) .... replace w with a+2
2wz = 2*(a+2)*(a) ... replace z with a
2wz = 2a(a+2)
2wz = 2a(a) + 2a(2) .... distribute
2wz = 2a^2 + 4a
The value of 2wz in terms of a is equal to [tex]2wz=2a^{2} +4a[/tex]
To understand more, check explanation below.
Linear equation:The equation is given as,
w = a +2 and z = a
We have to find 2wz.
[tex]2wz=2*w*z\\\\2wz=2*(a+2)*a\\\\2wz=2(a^{2}+2a )\\\\2wz=2a^{2} +4a[/tex]
The value of 2wz in terms of a is equal to [tex]2wz=2a^{2} +4a[/tex]
Learn more about the linear equation here:
https://brainly.com/question/14323743
Marcus is making homemade barbecue sauce.The recipe caps for 3 cups of ketchup for every 1/2 cup of mustard
Answers
Answer:
3 divided by 1/2
Step-by-step explanation:
turn 3 into 3/1 then flip 1/2 into 2/1 and multiply which is 6
Kcf
Keep
Change
Flip
What is the y-intercept of the equation y=3/4x-1
Answers
Answer:
y-intercept for this equation is -1.
What is the selling price of a $610 couch with a 25% markup?
a. $152.5b. $762.5c. $457.5d. $798.5
pls answer quickly ! :(
Answers
Answer:
762.5
Step-by-step explanation:
25% of 610 is 152.5 and 610 + 152.5 is 762.5
Hope this helped also can i get brainliest?
math question please help!!!
Answers
Answer:
i think it c
Step-by-step explanation:
sorry if i wrong
what is the factor of 6a2 – 19a + 10 ???
Answers
Answer:
(2a - 5) • (3a - 2)
step by step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 6 • 10 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -19 .
-60 + -1 = -61
-30 + -2 = -32
-20 + -3 = -23
-15 + -4 = -19 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and -4
6a2 - 15a - 4a - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
3a • (2a-5)
Add up the last 2 terms, pulling out common factors :
2 • (2a-5)
Step-5 : Add up the four terms of step 4 :
(3a-2) • (2a-5)
Which is the desired factorization
Final result :
(2a - 5) • (3a - 2)
Answer:
(2a-5) (3a-2) is your correct answer.thank you ☺️☺️