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:
Concave Up: (-∞, 1)
Concave Down: (1, ∞)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Combining Like TermsCalculus
Derivative of a Constant is 0.
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Second 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.IStep-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 + 6Step 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 = 1Step 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) = 6This 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) = -6This 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) = 0So 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
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
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
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To hard me brain go BOOM
Step-by-step explanation:
lol sorry i cant
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Answer:
d.
Step-by-step explanation:
Answer:
D
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
By which rule are these triangles congruent?
Answers
Answer:
sss
Step-by-step explanation:
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)
List all sets that -1/3 belongs to.
Answers
Answer:
dfffffffff
Step-by-step explanation:
xcdsw23456iu76
0.3, 0.08, 0.003, 0.83
In order from smallest to largest
Answers
Answer:
0.003, 0.08, 0.3, 0.83
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 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:
28
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
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
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
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!
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
11/15
14/15
2/3
2/3
5/7
hope this helps!!!
Please help!! algebra
Find each value
1. ∛x³
2. 6³
3. 10³
Answers
216
1000
Hope it helps:)
PLEASEEEE HELPPP MEEE :(
Answers
Answer:
Question 5 is B
Because after I simplified I got B and its the only one that makes sense.
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:
c
Step-by-step explanation:
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
The reason:if you add 10+30=40 then 30+10=40 then 40+40=80 last 100+80=180
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.
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:
C
Step-by-step explanation:
i lied :)
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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.
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:
66
Step-by-step explanation:
50% = 1/2
33 x 2 = 66
what is the meaning of function
Answers
Answer:
A relationship or expression involving one or more variables
Step-by-step explanation:
One day Clare runs 4 miles. The next day she
runs 50% of that. How far does she run in total?
Answers
Answer:
She runs 6 miles in total.
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.A. TrueB. False
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.
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.
Read more;
https://brainly.com/question/11966980
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. ;)
pattern 60 52 44 36
Answers
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.
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
Plug it in: y = -3x + b
1 = -3(-2) + b
1 = 6 + b
b = -5
Final equation: y = -3x -5