help please!
figure out the "inflection point" of the following function
f(x)=5x³ + 2x² − 3x​

Answers

Answer 1

Answer:

x = -2/15.

Step-by-step explanation:

Finding the second derivative:

f'(x) = 15x^2 +4x - 3

f"(x) = 30x + 4

30x + 4 = 0   for a point of inflection

x = -4/30 =  -2/15

So 30x + 4 is negative up to x =  -2/15 and positive thereafter.

So the curve passes from concave downward to concave upward at x = -2/15.

Answer 2

Answer:

[tex] \displaystyle \left( - \frac{2}{15} , \frac{286}{675} \right)[/tex]

Step-by-step explanation:

to figure out the infection point

take derivative both sides:

[tex] \displaystyle f'(x) = \frac{d}{dx} {5x}^{3} + 2 {x}^{2} - 3x[/tex]

By sum derivation rule we acquire:

[tex] \displaystyle \rm f'(x) = \frac{d}{dx} {5x}^{3} + \frac{d}{dx} 2 {x}^{2} - \frac{d}{dx} 3x[/tex]

apply exponent derivation rule which yields:

[tex] \displaystyle f'(x) = {15x}^{2} + 4{x}^{} - 3[/tex]

take derivative in both sides once again which yields:

[tex] \rm\displaystyle f''(x) = \frac{d}{dx} {15x}^{2} + \frac{d}{dx} 4{x}^{} - \frac{d}{dx} 3[/tex]

remember that, derivative of a constant is always 0 so,

[tex] \rm\displaystyle f''(x) = \frac{d}{dx} {15x}^{2} + \frac{d}{dx} 4{x}^{} - 0[/tex]

by exponent derivation rule we acquire:

[tex] \rm\displaystyle f''(x) = {30x} + 4{}^{} [/tex]

substitute f''(x) to 0 figure out the x coordinate of the inflection point:

[tex] \rm\displaystyle {30x} + 4{}^{} = 0[/tex]

cancel 4 from both sides:

[tex] \rm\displaystyle {30x} = - 4[/tex]

divide both sides by 30:

[tex] \rm\displaystyle {x} = - \frac{2}{15} [/tex]

now plugin the value of x to the given function to figure out the y coordinate of the inflection point:

[tex] \rm \displaystyle f(x) = {5 \left( - \frac{2}{15} \right) }^{3} + 2 {\left( - \frac{2}{15} \right) }^{2} - 3 \left( - \frac{2}{15} \right)[/tex]

By simplifying we acquire:

[tex] \displaystyle f(x) = \frac{286}{675} [/tex]

hence,

the coordinates of inflection point are

[tex] \displaystyle \left( - \frac{2}{15} , \frac{286}{675} \right)[/tex]


Related Questions

Can anyone help ? I’m bad at math

Answers

Answer:

Step-by-step explanation:

First you need the third angle (C).

<C + 89  + 45 = 180       All triangles = 180 degrees. Combine the left terms.

<C + 134 = 180               Subtract 134 from both sides

<C = 180 - 134

<C = 46

Next, Let BA = x

x/Sin(46) = 15/Sin(89)

x = 15*sin(46) / Sin(89)

Sin(46) = 0.7193

Sin(89) = 0.9998

x = 0.7193 * 15 / 0.9998

x = 10.7911

Note

When you are studying this material, you should note 2 things.

The first is that you are dealing with 2 ratios that are equal to each other.The second is, the side is always opposite the angle in the triangle. The two are connect. Side c = 15. It is opposite the 89o angle.

Solve the equation. Then check your solution. – two-fifths + a = One-fifth a. Three-fifths c. StartFraction 3 Over 10 EndFraction b. Negative one-fifth d. Negative three-fifths Please select the best answer from the choices provided A B C D

Answers

Answer:

A . a = 3/5

Step-by-step explanation:

- 2/5 + a = 1/5

Add 2/5 to each side

-2/5 + a + 2/5 = 1/5 + 2/5

a = 3/5

Therefore a = 3/5

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

12. You are measuring the height of a Sitka spruce tree in Alaska. You stand 45 feet from the base of
the tree. You measure the angle of elevation from a point on the ground to the top of the tree
to be 59º. Estimate the height of the tree.

Answers

Answer:

tangent 59° = Tree height / 45 feet

Tree Height = 1.6643 * 45

Tree Height = 74.8935 Feet

Step-by-step explanation:

Please help me with this!!!!!!!!!!!!!!! MATHHHHHH

Answers

I can’t see anything on the screen

find the x intercept of 3x²-5x-28=f(x)

Answers

Answer:

x+ 4, -7/3

Step-by-step explanation:

Find the area of the trapezoid 12in 11in 8in???

HELP ME PLEASE!!!​

Answers

Answer:

formula: A= a+b/2 times height

So 12+8=20/2=10x11=110

Step-by-step explanation:


10) A 15% tip is left on a $72.25 dinner bill. How
much is the tip? Round to the nearest hundredth

Answers

10.84...................

plz plz help me for math

Answers

Answer:

Oasis idiot and a good time in the day before

find the rational number between-5/6 and -3/8
help me​

Answers

Answer:

-2/5

-4/9

Step-by-step explanation:

-5/6 = -0.83333 (three's keep repeating)

-3/8 = -0.375

the above are both rational because they result in a repeating or terminating decimal

There are an infinite number of  rational numbers between the two listed above but here are some:

-2/5 = -0.40  (terminates)

-4/9 = -0.4444444 (fours keep repeating)

-1/2 = -0.50 (terminates)

-3/4 = -0.75 (terminates)

A boy has a weekend job advertising an upcoming play. He has 2 options for being paid. Option A is an hourly wage of $7.00. Option B is a 5% commission on all money made at the play she plans to work 8 hours each day on Saturday and Sunday. He estimates the play will make about $2,100 this weekend. Which option gives him more earnings this weekend?

Answers

Answer:

He would be paid more if he took the hourly wage//option A

Step-by-step explanation: hope this helps<3

sunita has to ribbons of lengths 25 inches and 35 inches he want to cut the Ribbon into strips of equal length what is the longest possible length for the strips​

Answers

Answer:

5 cm

Step-by-step explanation:

Need explanation for this question please

Answers

The answer to this question is D.

A rental car company charges $53.75 per day to rent a car and $0.12 for every mile driven. Jaya wants to rent a car, knowing that: She plans to drive 125 miles. She has at most $230 to spend. Write and solve an inequality which can be used to determine xx, the number of days Jaya can afford to rent while staying within her budget.

Answers

Answer:

Jaya can afford to rent a car 4 days while staying within her budget.

Step-by-step explanation:

The inequality would have to indicate that the cost of renting a car has to be less than or equal to $230. The cost to rent a car is equal to the cost per day for the number of days plus the price per mile for the number of miles, which is:

53.75x+0.12y≤230, where:

x is the number of days the car is rented

y is the number of miles driven

As the statement says that she plans to drive 125 miles, you can replace "y" with this value and solve for x:

53.75x+0.12(125)≤230

53.75x+15≤230

53.75x≤230-15

53.75x≤215

x≤215/53.75

x≤4

According to this, the answer is that Jaya can afford to rent a car 4 days while staying within her budget.

. If Shawn rides his bike ¾ mile every ½ hour, how many miles does he bike per hour?

Answers

Answer:

1 1/2 mile or 6/4 mile

Step-by-step explanation:

Every half hour he rides 3/4

Just multiply 3/4 by 2 which equals 6/4 or 1 1/2

Help!! It's question 14

Answers

Answer:

200/120 = 5/3

5/3 x 3 = 5 oz

you can also do it this way:

3/120 = x/200

x = 600/120 = 5

Determine the y-intercept of the following equation. help pls​

Answers

Answer:

0,8

Step-by-step explanation:

(-x-2)(x-4)=y

To find the x-intercept, substitute in 0 for y and solve for x. To find y-intercept, substitiue in 0 for x and solve for y.

(-0-2)(0-4)=y

(-2)(-4)=8

y=8

0,8

Which of the expressions below is equal to 24/18? Select all that apply.Which of the expressions below is equal to 2418? Select all that apply.

Answers

Answer:

A, B, D

Step-by-step explanation:

Given that :

24 / 18 = 4 / 3 = 1.333

Comparing the options solutions for the options given :

3/9 ÷ 2/8 = 3/9 * 8/2 = 24 / 18 = 1.333

4/9 ÷ 2/6 = 4/9 * 6/2 = 24/18 = 1.333

5/6 ÷ 3/4 = 5/6 * 4/3 = 20 / 18

8/3 ÷ 6/3 = 8/3 * 3/6 = 24 / 18 = 1.333

Hence, expressions which are equal are :

A, B and D

What is the answer to this?

Answers

Answer:

Area = 1514 m^2

Step-by-step explanation:

Total Area = area of rectangle + area of circle

= (60 m × 20 m) + πr^2

= (1200 m^2) + (3.14)(10 m)^2

= (1200 m^2) + (314 m^2)

= 1514 m^2

is this a polygon or not a polygon

Answers

This is not a polygon as it has a section (at the bottom) which is composed of non-straight segments.

There are two precalculus sections at a high school. Mr.​ Abel's class has 14 girls and 8 ​boys, while Mr.​ Bonitz's class has 12 girls and 12 boys. If a precalculus student chosen at random happens to be a​ girl, what is the probability she is from Mr.​ Abel's class?

Answers

Answer:

14/46

Step-by-step explanation:

Find the sum of the series please

Answers

Answer:

12

Step-by-step explanation:

This is considered a geometric series.

a = 4

r = 2/3

[tex]Sum = \frac{a}{1-r}[/tex]

[tex]Sum = \frac{4}{1-\frac{2}{3} } =12[/tex]

Take(10 2+7−3)from(4 2−9+12)

Answers

Answer: -13

How to: Simplify the expression.

Answer:

0 is less than 2 is equal to 2

0/

1

< 2/

1

= 2/

1

The list price of a furnace is $2,468.00. The manufacturer offers a discount of 15 percent. The net price is

$2,097.80.

$370.20.

$209.78.

$3,702.00.

Answers

Answer:2,097.80

Step-by-step explanation: If you multiply the 2,468.00 to 0.85% you will get the answer of 2,097.80.

Answer:

$2,097.80

Step-by-step explanation:

$2,468.00 - 15%

$2,468.00 * 0.15 = $370.20

$2,468.00 - $370.20 = $2,097.80

(Just another way to do it)

Find the number of unique permutations of the letters in each word.
5) CORRIDOR
6) NUMBER

Answers

Answer:

Ur Answer is 5 one CORRIDOR

The number of unique permutations of the letters CORRIDOR is 3360

The number of unique permutations of the letters NUMBER is 720

What is Permutation?

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.

[tex]\frac{n!}{mA!mB!......mZ!}[/tex]

In the given word

CORRIDOR

There are 7 letters in which "O" repeats 2 times and "R" repeats 3 times.

Then n = 7 , A = 2 and B = 3

Put values in above formula

Then,

=  [tex]\frac{7!}{2!3!}[/tex]

= [tex]\frac{7\times6\times5\times4\times3\times2\times1}{2\times3\times2}[/tex]

= 3360

Similarly

NUMBER

There are 6 letters in which no letter repeats

means A = B = .......= Z = 1

Put values in above equation

= [tex]6![/tex]

= 720

Hence,

The number of unique permutations of the letters CORRIDOR is 3360.

The number of unique permutations of the letters NUMBER is 720.

Learn more about permutation:

https://brainly.com/question/121616

#SPJ2

The train is travelling with the speed of 90km/hr. What is the distance covered in 2min?​

Answers

We are given:

Speed of the train = 90 km/h

Converting the speed to km per minute:

[tex]90\frac{km}{h}* \frac{h}{60 min}[/tex]           [since 1 hour = 60 minutes, h/60 minutes is equal to 1]

The 'h' in numerator and denominator will cancel out

90km / 60 min

1.5 km/min

Distance travelled in 2 minutes:

Distance = Speed * time

Distance = [tex]1.5\frac{km}{min}* 2 min[/tex]

Distance = 3 km

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $8 and each adult ticket sells for $11.50. The auditorium can hold at most 81 people. The drama club must make at least $760 from ticket sales to cover the show's costs. If 43 student tickets were sold, determine the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses. If there are no possible solutions, submit an empty answer.

Answers

Answer:

the closest I found was 79

Step-by-step explanation:

8×43=344

760-344=416

416÷11.5=36.173

36+43=79

please help in this........​

Answers

Helloo!

I founded same type of question from Brainly! People who have been written this solving questions. Also search and check for this question on Brainly!! Or my advice to download course hero because there is so many subjects that you can work on it.

GIVEN THAT AD = 5 and BC = 24, what is the radius of circle A?

Answers

Answer:

12

Step-by-step explanation:

B to C looks like your diameter so half of 24 is 12.

Which expression represents the following?

Add 450 to 348, and then multiply by 7.

Answers

Answer:

(450 + 348) · 7

equals 5586

Step-by-step explanation:

find the answer of 450 and 348, then multiply the answer by 7

Answer:

(450 + 348) x 7

Step-by-step explanation:

1. a box contains 11 pink 8 blues and 9 orange marbles. If you pick two marbles without looking , what is the probability that the first will be orange and the second will be pink?

2. You accidentally dropped a coin from the top of 10 stairs. What is the probability that it will land heads up on the seventh step?

Answers

1. the probability of picking an orange marble is 35% and the probability of picking a pink marble second would be 66%

2. the probability is about 47%
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