Determine the value of c, given that the graph of f(x) = cx^2 + 1/x^2
has a point of inflection at (1, f(1))

Answers

Answer 1

Answer:

The value of c is [tex]c = \frac{1}{3}[/tex]

Step-by-step explanation:

Point of inflection:

A function f(x) has a point of inflection at the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

Has a point of inflection at (1, f(1))

This means that [tex]f^{\prime}(1) = 0[/tex]

f(x) = cx^2 + 1/x^2

This means that, applying the derivative of a power rule:

[tex]f^{\prime}(x) = 2cx - \frac{2}{x^3}[/tex]

Since [tex]f^{\prime}(1) = 0[/tex]

[tex]2c - \frac{2}{3} = 0[/tex]

[tex]2c = \frac{2}{3}[/tex]

[tex]c = \frac{2}{2*3} = \frac{1}{3}[/tex]

The value of c is [tex]c = \frac{1}{3}[/tex]


Related Questions

1
The area of a square window is
given by the expression
m’ - 16m+64. Which expression
represents the length of one side
of the window?
a)m - 8
b) m + 4
c)m - 4
d) m + 8

Answers

Answer:

Step-by-step explanation:

-8 ok!

Use the passbook page to answer the question.
Name Ken Ritter
Account 10000000004
Date Deposit Withdrawal Interest Balance
1/02/06 $389.00
$389.00
2/05.06 $25.63
A
3/02/06 $122.33
B
4/02/06
$240 С
4/15,06
$500.00
D
5/06/06 $105.00
E
Ken Ritter was saving for a computer.
What was his balance B after he made two deposits?
O $526.36
o S536.96
OS554.26
O S636.86

Answers

Answer:

the answer is 536.96

its asking for you to add the balance (389) with the 2 deposits (25.63, 122.33)

hope this helps

which rule descibes the pattern?

Answers

Answer:

-1/2

Step-by-step explanation:

I think not 100% sure tho

Answer:

“multiply by 2 and then subtract 1.

Step-by-step explanation:

Domain and range of graph need ASAP

Answers

Answer:

Domain: [tex]-6 \leq x \leq 3[/tex]

Range: [tex]-3 \leq x \leq 6[/tex]

Step-by-step explanation:

The domain is the set of real values which can be inputted into a function and produce a real output. In this case, the domain is the following: [tex]-6 \leq x \leq 3[/tex], because this is the set of real values for which the function will produce a real output.

The range is the set of real values which a function outputs when a value from the domain is entered into the function. This is the set of y-values that one can see on the graph, the possible y-values are in between (-3) and (6).

A customer at Lost Pastores placed an order for 3 burritos which was priced at x amount of dollars each. He also ordered a plate of corn tacos for $12.95. His total bill was $32.46.as

Answers

Answer:

3x +12.95 = 32.46

Step-by-step explanation:

3 burritos plus x + 12.95 = $32.46

Answer:

i don't know lololololol

Step-by-step explanation:

A kite was broken into two triangles of the same size and shape .
The area of each triangle is ? Square centimeters
20,40,80,160
The total are of the kite is ? Square centimeters
40,80,160,320

ANSWER_
The answers are 40 and 80

Answers

Answer:

hey the answer is 402

Step-by-step explanation:

Answer:

40 and 80

Step-by-step explanation:

got it on edgenuit y

Find the product, explain it in words.

-5 x (-2/5)

Answers

-5 x (-2/5)
Using PEMDAS, solve for parenthesis first (divide)
-5 x (-0.4)
Multiply
Solution: 2

Answer:

The answer will be 2

Step-by-step explanation:

The way you find the answer is by multiplying the numbers (simplifying)

Canceling both of the fives and adding the two negative signs together would leave you with the product of 2

To the nearest 1000, there are 18,000 people at a festival . Write down the minimum possible number of people at the festival

Answers

Answer:

17500

Step-by-step explanation:

17499 rounds down

17500 rounds up

The number of people is an illustration of approximation and estimation

The minimum possible number of people at the festival is 17500

The approximated number of people is:

People  = 18000

Because 18000 represents people, it means that the population is a whole number

The smallest whole number that can be approximated to 18000 is 17500

i.e.

People = 17500

Hence, the minimum possible number of people at the festival is 17500

Read more about approximation and estimation at:

https://brainly.com/question/24586443

Which of these is equivalent to 12x + 6 ? Select all.
A. 3(4x + 2)
B. 6(2x + 1)
C. 6x(2x + 1)
D. 2(6x + 3)

Answers

Answer:

A

Step-by-step explanation:

are there mutiple answers possible? if so, then
A, B and D are right

In the last several weeks, 18 days saw rain and 29 days saw high winds. in the same time period 7 days saw both rain and high winds. How many days saw either rain or high winds

Answers

Answer:

40 days saw either rain or high winds

Step-by-step explanation:

We solve this question using Venn sets.

I am going to say that:

Set A: Rain

Set B: High winds.

18 days saw rain

This means that [tex]A = 18[/tex]

29 days saw high winds

This means that [tex]B = 29[/tex]

7 days saw both rain and high winds.

This means that [tex]A \cap B = 7[/tex]

How many days saw either rain or high winds?

This is

[tex]A \cup B = A + B - A \cap B[/tex]

Sp

[tex]A \cup B = 18 + 29 - 7 = 40[/tex]

40 days saw either rain or high winds

1) A population of bees is increasing at a rate of 8% per week. If
the population had an original size of 250 bees. Then how many
bees will there be after 10 days? (state equation)

Answers

Answer:

≈387,7

Step-by-step explanation:

I hope it's right. Sorry if it's not right.

Juan determines that a triangle has sides that measure 5 cm, 12 cm, and 13 cm. The same triangle also has one 90°° angle and two angles that are less than 90°°. Which best describes the triangle Juan is measuring?
isosceles right

scalene acute

scalene right

equilateral right

Answers

Answer:

scalene right

Step-by-step explanation:

A scalene right has no equal side lengths, has a right side(90) and will have two angles less than 90 because all three triangle sides need to equal to be 180. So scalene right is your answer. Hope that helped!

Pls helppp ASAP pls

Answers

Answer:

Four (4); 45; at least; 181.

Step-by-step explanation:

Ali has four friends that owe him x dollars each. His parents owe him $45 for doing chores last week. He recalls that people owed him at least $181.

To find how much money each of Ali's friends owe him;

Given the algebraic expression;

4x + 45 ≤ 181

4x ≤ 181 - 45

4x ≤ 36

Dividing both sides by 9, we have;

x ≤ 9

Therefore, Ali's friends owe him at least $9 each.

Answer:

Four (4); 45; at least; 181.

Step-by-step explanation:

Hope this helps

124,567 is closer to 100,000 than 200,000

Answers

if you’re asking if it’s true or false, then it’s true

what is the simple ratio of 1 ½km to 900m​

Answers

I think it would be 1:600

the question is in the picture ​

Answers

the answer is third one

What are the coordinates of each point after quadrilateral ABCD is reflected across the y-axis and then translated 2 units down? Drag numbers 1

complete the coordinates Numbers may be used once, more than once, or not at all

Answers

Answer:

[tex]A" = (3,2)\ \ B" = (-1,1)\ \ C" =(-3,4)\ \ D =(-1,4)[/tex]

Step-by-step explanation:

Given [Missing]

[tex]A = (-3,4)[/tex]

[tex]B = (1,3)[/tex]

[tex]C =(3,6)[/tex]

[tex]D =(1,6)[/tex]

The first transformation: reflection across the y-axis.

The rule is: [tex](x,y)==>(-x,y)[/tex]

So:

[tex]A = (-3,4)[/tex] ==>[tex]A' = (3,4)[/tex]

[tex]B = (1,3)[/tex] ==> [tex]B' = (-1,3)[/tex]

[tex]C =(3,6)[/tex] ==> [tex]C' = (-3.6)[/tex]

[tex]D =(1,6)[/tex] ==> [tex]D' = (-1,6)[/tex]

Translation 2 units down

The rule is: [tex](x,y)==>(x,y-2)[/tex]

So:

[tex]A' = (3,4)[/tex] ==> [tex]A" =(3,4-2) =(3,2)[/tex]

[tex]B' = (-1,3)[/tex] ==> [tex]B" = (-1,3-2) = (-1,1)[/tex]

[tex]C' = (-3.6)[/tex] ==> [tex]C" = (-3,6-2) = (-3,4)[/tex]

[tex]D' = (-1,6)[/tex] ==> [tex]D" =(-1,6-2) = (-1,4)[/tex]

Hence:

[tex]A" = (3,2)\ \ B" = (-1,1)\ \ C" =(-3,4)\ \ D =(-1,4)[/tex]

What are the three ordered pairs that should be in the table of values y=2x-3

Answers

Answer:

(-2, -7), (0, -3), (2, 1)

Step-by-step explanation:

Equation is given as y = 2x - 3.

To complete the table, plug in each value of x into y = 2x - 3 to get their corresponding y-value.

✔️When x = -2:

y = 2(-2) - 3

y = -4 - 3

y = -7

✔️When x = 0:

y = 2(0) - 3

y = -3

✔️When x = 2:

y = 2(2) - 3

y = 4 - 3

y = 1

Is (x-4) a factor of x^3 +x^2 -16x-16x 3 +x 2 −16x−16 ?

Answers

Answer:

For x – 4 to be a factor, you must have x = 4 as a zero. Using this information, I'll do the synthetic division with x = 4 as the test zero on the left:

Step-by-step explanation:

A circle has a radius of 48 millimeters.

What is the length of the arc intercepted by a central angle that measures 3π4 radians?

Express the answer in terms of π .

Answers

Answer:

36pi mm

Step-by-step explanation:

A circle has 2pi radians so 3pi/4 is 3/8 of it. The circumference is 96 mm so the length of the arc is 36pi mm.

Answer:

36π

Step-by-step explanation:

zero has how many square roots? Why?

Answers

Answer:

Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0.

Step-by-step explanation:

Milan has a total of 51 nickels and dimes worth $4.95. How many of each coin does she have?

Answers

Answer: 75 coins total, 51 nickels and 24 dimes.

Step-by-step explanation:

atomic structure escape room level 2 (HELP ASAP!!) what does each one lead to

Answers

Answer:

2c 1d 3b 4a is this for your schoooooools

The floor of a storage unit is 6 ft long and 8 feet wide what is the distance between two opposite corners of the floor

Answers

Answer:

10 ft

Step-by-step explanation:

Use theorem pythagoras

Length = x

[tex] {x}^{2} = 8 {}^{2} + {6}^{2} \\ x = - 10 \\ x = 10[/tex]

the answer is 10 because length can't be in negative number

giving brainliest !! *easy*

Answers

I believe that the center is located at (1,-3) and the radius is 3.

um here’s the graph

In a right angled triangle , one acute angle is 30°. Find the other acute angle

Answers

As it is right angled triangle , Other acute angle = 180-(30+90)= 60°.
Answer:
60

Explanation:
30 + 90 = 120
180 - 120 = 60

Identify the slope and y-intercept of the line.
8x - 3y = 12

Answers

Answer:

y=8/3x-4

Step-by-step explanation:

use the app photomath to get the answers or socratic there free and will help you on homework or tests

Answer:

Step-by-step explanation:

8x-3y=12

-3y=12-8x

y=(12/-3)-8x/(-3)

y= -4+8/3x

slope= 8/3

y-int=-4

Pls help you will get brainlist if ya do

Answers

The x and y coordinate are switched

What is the length of PR?

Answers

Answer: The length of PR is 7 units.

Step-by-step explanation:The length of PR is 7 units.

Answer:

A.7

Step-by-step explanation:

Square Root Equation! HELP ME!!!!

Do not scam or false answers.

Answers

the 2nd one is 5 because 5x5 or 5 squared is equal to 25. and the first one i’m not sure of
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