Mathematics College

The graph of f (x) = −x3 + 3x2 − 2 is
shown in the figure to the right.
Complete the table below by using
the second derivative of f to identify
the intervals on which f us concave
upward or concave downward and
to identify the inflection points of f.

Answers

Answer 1

Answer:

Concave Up: (-∞, 1)

Concave Down: (1, ∞)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Combining Like Terms

Calculus

Derivative of a Constant is 0.

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Second Derivative Test:

Possible Points of Inflection (P.P.I) - Tells us the possible x-values where the graph f(x) may change concavity. Occurs when f"(x) = 0 or undefinedPoints of Inflection (P.I) - Actual x-values when the graph f(x) changes concavityNumber Line Test - Helps us determine whether a P.P.I is a P.I

Step-by-step explanation:

Step 1: Define

f(x) = -x³ + 3x² - 2

Step 2: Find 2nd Derivative

1st Derivative [Basic Power]: f'(x) = -1 · 3x³⁻² + 2 · 3x²⁻¹Simplify: f'(x) = -3x² + 6x2nd Derivative [Basic Power]: f"(x) = -3 · 2x²⁻¹ + 1 · 6x¹⁻¹Simplify: f"(x) = -6x + 6

Step 3: Find P.P.I

Set f"(x) equal to zero: 0 = -6x + 6Isolate x term: -6 = -6xIsolate x: 1 = xRewrite: P.P.I x = 1

Step 4: Number Line Test

See Attachment.

We plug in the test points into the 2nd Derivative and see if the P.P.I is a P.I.

x = 0

Substitute: f"(0) = -6(0) + 6Multiply: f"(0) = 0 + 6Add: f"(0) = 6

This means that the graph f(x) is concave up before x = 1.

x = 2

Substitute: f"(2) = -6(2) + 6Multiply: f"(2) = -12 + 6Add: f"(2) = -6

This means that the graph f(x) is concave down after x = 1.

Step 5: Identify

Since f"(x) changes concavity from positive to negative at x = 1, then we know that the P.P.I x = 1 is actually a P.I x = 1.

Let's find what actual point on f(x) when the concavity changes.

Substitute in P.I into f(x): f(1) = -(1)³ + 3(1)² - 2Evaluate Exponents: f(1) = -(1) + 3(1) - 2Multiply: f(1) = -1 + 3 - 2Combine like terms: f(1) = 0

So at (1, 0), f(x) changes concavity from concave up to concave down.

Step 6: Define Intervals

We know that before f(x) reaches x = 1, the graph is concave up. We used the 2nd Derivative Test to confirm this.

Concave Up Interval: (-∞, 1)

We also know that after f(x) passes x = 1, the graph is concave down. We used the 2nd Derivative Test to confirm this as well.

Concave Down Interval: (1, ∞)

Related Questions

What is the equation of a line that is perpendicular to 2x+y=−4 and passes through the point (2, −8) ?

Answers

Answer:

y=1/2z-9= Perpendicular line

y=-2x-4= parrallel

Step-by-step explanation:

Answer:

y = [tex]\frac{1}{2}[/tex] (x) - 9

Step-by-step explanation:

Set the given equation to standard form: y = -2x -4

Set the slope of the given equation's slope to the reciprocal ( -2 --> 1/2).

Thus, you will have y = 1/2x + b

Insert the given information: (2, -8)

-8 = 1/2 (2) + b

Half of 2 is 1: subtract it on both sides...

-8 = 1 + b

-1 -1

-9 = b

So, the equation will be y = 1/2(x) - 9

Write the slope intercept form of the equation of the line through the given point with the given slope

Through: (-2,1), slope = -3

Answers

Slope form: y= mx + b
Plug it in: y = -3x + b
1 = -3(-2) + b
1 = 6 + b
b = -5
Final equation: y = -3x -5

Please help!
Thanks in advance.

Answers

Answer:

y = (1/4)x + 5/2

Step-by-step explanation:

The lines slope needs to be opposite of the equation's so its positive (1/4)

This is the only slope listed that is that number so no need to calculate for the y value!

Vocabulary How can you tell when an equation in one variable has infinitely many solutions or no solution? When you solve for the variable, you will end up with a true statement, like 2 = 2, for an equation with no solution. You also will end up with a true statement for an equation with infinitely many solutions. When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will also end up with a false statement for an equation with infinitely many solutions. When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will end up with a true statement, like 2 = 2 for an equation with infinitely many solutions. When you solve for the variable, you will end up with a true statement, like 2 = 2, for an equation with no solution. You will end up with a false statement, like 0 = 2 for an equation with infinitely many solutions.

Answers

Answer: Choice C) When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution. You will end up with a true statement, like 2 = 2 for an equation with infinitely many solutions.

For example, let's say we had the equation x = x+2. Subtracting x from both sides leads to 0 = 2 which is a false statement. No matter what we replace x with, the equation x = x+2 is always false. That's why we don't have any solutions here.

For an equation like x + 2 = x + 2, subtracting x from both sides leads to 2 = 2 which is always true. A true equation is one where the same number is on both sides. No matter what we replace x with, the equation will be true. Therefore, there are infinitely many solutions.

To tell when an equation in one variable has infinitely many solutions or no solution;

When you solve for the variable, you will end up with a false statement, like 0 = 2, for an equation with no solution.

You will end up with a true statement, like 2 = 2 for an equation with infinitely many solutions.

The condition for an equation with no solution warrants that the equation upon evaluation yields a false statement as in the case of 1 = 2. In this case, such an equation has no solution.

The condition for an equation with infinitely many solutions warrants that the equation upon evaluation yields a true statement as in the case of y + 5 = y + 5. In this case, such an equation has infinitely many solution.

Answers

Answer:

The statement provided is False.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

We use the paired t-test if we have two measurements on the same item, person or thing. We should also use this test if we have two items that are being measured with a unique condition.

For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.

The statement provided is:

"A paired t-test can be treated as an inference about the mean of differences between two experimental conditions for a single sample of independent subjects."

Thus, the statement provided is False.

50% of trick or treaters dressed up as a ghosts.
You have seen 33 ghosts. How many trick or
treaters did you see in all?

Answers

Answer:

Step-by-step explanation:

50% = 1/2

33 x 2 = 66

By which rule are these triangles congruent?

Answers

Answer:

sss

Step-by-step explanation:

A taxi company charges $2.25 for the 1st mile and then $0.20 per mile for each additional mile, or F= $2.25+ $0.20 (m-1) where F is the fare and m is the number of miles. If Juan’s taxi fare is $7.65 ,how many miles did he travel in the taxi?

Answers

Answer:

Step-by-step explanation:

F=2.25+0.20(m-1)

7.65=2.25+0.20(m-1)

5.4=0.20(m-1)

5.4/0.20=0.20(m-1)/0.20

27=m-1

28=m

what is the meaning of function

Answers

Answer:

A relationship or expression involving one or more variables

Step-by-step explanation:

pattern 60 52 44 36

Answers

Decreasing by 8 each time

List all sets that -1/3 belongs to.

Answers

Answer:

dfffffffff

Step-by-step explanation:

xcdsw23456iu76

A car running at a constant speed covers a distance of 492.36 km in
12 hours. Calculate the distance covered by the car in 51/2 hours.

Answers

Answer:

the anser is 1046.265 because in

492.36=12hour

? =51/2hour then criscros both side 492.36*25,5/12=492.36

Math problem pls help I will give brainiest

Answers

Answer:

y=5

Step-by-step explanation:

125 +125+13y+9y=360

punch it into math-way.

250+22y=360

22y= 110

y=5

Add the two expressions.

3z−4 and 2z + 5

I need it asap please help!

Answers

Answer:

3(1)-4=-1 2(1)+5=7

Answer:

5z+1

Step-by-step explanation:

it was simple

I'll braintlist!!!
Find the value of each expression in lowest terms:

1/6 X 11/4

11/5 X 1/3

14/3 X 1/5

5/3 X 2/5

3/4 X 8/9

5/2 X 2/7

Answers

11/24
11/15
14/15
2/3
2/3
5/7
hope this helps!!!

We have a bag that contains 100 balls, 50 of them red and 50 blue. Select 5 balls at random. What is the probability that 3 are blue and 2 are red?

Answers

Answer:

Likely, I think I havent been in this for a long time so i may be a little rusty. But anyways, I hope this helped!

Step-by-step explanation:

32% is the probability that 3 are blue and 2 are red.

What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

We have a bag that contains 100 balls, 50 of them red and 50 blue.

We, Select 5 balls at random.

the probability that 3 are blue and 2 are red = 50C3*50C2/50C5

solving we get,

19600*1225/75287520

=24010000/75287520

=0.32

=32%

Hence, 32% is the probability that 3 are blue and 2 are red.

To learn more on probability click:

brainly.com/question/11234923

#SPJ2

A company order two types of games, board and electronic. A shipment
containing 4 board games and 5 electronic games costs $103. A second
shipment containing 5 board games and 3 electronic games costs $80. Find the
cost of the board games and the cost of the electronic games.

Answers

Answer:

Step-by-step explanation:

i lied :)

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write 3 numbers that make this inequality true: x>4

Answers

Answer:

8, 10, 24

(Basically every number above 4)

Answer:

5,6 and 7

> means more than or greater than.

In this situation, its asking for numbers greater than 5.

Hope this helps. ;)

Y=2x^3 linear or nonlinear

Answers

Answer: linear

Step-by-step explanation:

Answer:

LINEAR...................

Step-by-step explanation:

y=2x−3 is in slope intercept form for a linear equation, y=mx+b , where m is the slope and b is the y-intercept. The y-intercept is the point at which x=0 and y=−3 , which is point (0,−3) You can plot this point on your graph. The slope is can be described as riserun , and can be written as 21 . Start at (0,3)

PLEASEEEE HELPPP MEEE :(

Answers

Answer:

Question 5 is B

Because after I simplified I got B and its the only one that makes sense.

Find 3 consecutive odd integers such that 10 times the first is 59 more than the third?

Answers

Answer: The required three consecutive odd integers are 7, 9 , 11.

Step-by-step explanation:

Let x , x+2 , x+4 be the three consecutive odd integers.

As per given ,

10(x) = 59+x+4

⇒10x= 59+x+4

⇒ 9x= 63

⇒ x= 7 [ divide both sides by 7]

Hence, the required three consecutive odd integers are 7, 9 , 11.

HELPP!! ITS A LOT BUT YOU GET POINTS!

Answers

Answer:

To hard me brain go BOOM

Step-by-step explanation:

lol sorry i cant

B.F. Retread, a tire manufacturer, wants to select one of three feasible prototype designs for a new tire; A, B, C.

Revenues
Low (0.30) Medium (0.50) High (0.20)
A 120,000 255,000 390,000
B 130,000 295,000 460,000
C 100,000 300,000 480,000

Required:
Calculate the highest value you would pay for a highly reliable forecast.

Answers

Answer:

Step-by-step explanation:

The value of 8 in 5.18 is
of the value of 8 in 5.81.

Answers

Answer: This is false.

Step-by-step explanation:

The value of 8 in 5.18 is 8 Hundredths, the value of 8 in 5.81 is 8 Tenths.

why is earth known as diatomaceous Earth???
From biology

Answers

Answer:

Diatomaceous earth is made from the fossilized remains of tiny, aquatic organisms called diatoms. Their skeletons are made of a natural substance called silica. Over a long period of time, diatoms accumulated in the sediment of rivers, streams, lakes, and oceans. Today, silica deposits are mined from these areas.

Please help!! algebra
Find each value
1. ∛x³
2. 6³
3. 10³

Answers

x
216
1000
Hope it helps:)

:∫ PLZZ help ;⊃ plz no playing around I need actual answer

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

15/10 goes down to 3/2 divide 15 by 5

21/14 goes down to 3/2 divide 21 by 7

One day Clare runs 4 miles. The next day she
runs 50% of that. How far does she run in total?

Answers

Clare runs 2 miles. 6 miles total. 50% is also 1/2.

Answer:

She runs 6 miles in total.

I have $10 my mom gave me $30 my dad gave me $30 my aunt and uncle gave me $100 but I had another $10 so how much do I have

Answers

Answer:

$180

Step-by-step explanation:

10+30+30+100+10=180

You have 180

The reason:if you add 10+30=40 then 30+10=40 then 40+40=80 last 100+80=180

0.3, 0.08, 0.003, 0.83
In order from smallest to largest

Answers

0.003, 0.08, 0.3, 0.83

Answer:

0.003, 0.08, 0.3, 0.83

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The graph of f (x) = −x3 + 3x2 − 2 is shown in the figure to the right. Complete the table below by using the second derivative of f to identify the intervals on which f us concave upward or concave downward and to identify the inflection points of f.

Answers

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The graph of f (x) = −x3 + 3x2 − 2 is
shown in the figure to the right.
Complete the table below by using
the second derivative of f to identify
the intervals on which f us concave
upward or concave downward and
to identify the inflection points of f.