given the function f(x)=-2x^4-16x^3-36x^2, determine all intervals on which f is both decreasing and concave down
Answers
Answer:
(0, ∞)
Step-by-step explanation:
The only maximum, local or otherwise, is at x=0. Since the leading coefficient is negative, the function is decreasing and concave down for x-values greater than 0.
0 < x < ∞ . . . . . decreasing and concave down
__
Since the leading coefficient of this even-degree function is negative, it will have a generally ∩ shape. It will be decreasing to the right of any local maximum.
The first derivative is negative only for x > 0, so that is the only region where the function is decreasing. Since that x=0 is a local maximum, the function must be concave downward in that neighborhood.
__
The attached graph shows the function and its first and second derivatives. The function is concave down where the second derivative is negative, to the right of the right-most point of inflection.
_____
Additional comment
A graphing calculator provides a quick answer to a question like this. You can find the same answer algebraically.
The first derivative is ...
f'(x) = -8x^3 -48x^2 -72x = -8x(x^2 +6x +9) = -8x(x+3)^2
This has a zero at x=-3 where the graph of it touches the x-axis, but does not change sign. That means f(x) has a flat spot at x=-3, but is not decreasing except to the right of x=0.
The second derivative is ...
f''(x) = -24x^2 -96x -72 = -24(x^2 +4x +3) = -24(x +1)(x +3)
The second derivative will be negative for x < -3 and x > -1, to the left and right of the points of inflection. This means f(x) is concave upward only for -3 < x < -1, and concave downward everywhere else.
The function is concave downward and decreasing for x > 0.
Related Questions
PLEASE ANSWER!!
STEP BY STEP
In hockey standing, I went out for two points, takeout for one point and I lost count for zero points. And the first time games, the devil 15, last four and tied one game. If they continues at the same rate, how many points do they have accumulated after they have played a total of 80 games?
Answers
NO LINKS PLEASE. 10 POINTS! WHAT IS THE ANSWERs to THE SCREENSHOT? P.S. Please include graphing and labeling<:
Answers
Answer:
The answer is located in the image below.
how do you solve 9-3(5-4x)
Answers
Answer:
-6+12x
Step-by-step explanation:
9-15+12xmultiply -3(5-4x), calculate the difference
-6+12x
Raven was a writing a story. She was trying to figure out how long it would take for her to write it. If she can ride 2 2/3 pages in one hour, how many pages will she have written after 2 1/2 hours? who is correct?
Answers
Answer:
She would have written 6 2/3 pages.
Step-by-step explanation:
2 2/3 pages = 1 hour
6 2/3 pages = 2 1/2 hours
HELPPP Provide the missing statements and reasons for the following proof:
Given: Line m is parallel to line n.
Prove: ∠1 is supplementary to ∠2.
Answers
The missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:
S2: ∠2 ≅ ∠3
R2: corresponding angles
S3: m∠2 ≅ m∠3
R3: Definition of congruent angles
R5: Definition of supplementary angles
S7: m∠1 + m∠2 = 180°
S8: ∠1 is supplementary to ∠2
Given the proof to show that ∠1 is supplementary to ∠2, thus:
Since lines m and n are parallel to each other,
∠2 and ∠3 are corresponding angles, so, ∠2 ≅ ∠3 based on the corresponding angles theorem.
Since ∠1 and ∠3 form a linear pair, they are supplementary to each other.
By substitution, we would have m∠1 + m∠2 = 180°.
Therefore, we can conclude that ∠1 is supplementary to ∠2.
In summary, the missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:
S2: ∠2 ≅ ∠3
R2: corresponding angles
S3: m∠2 ≅ m∠3
R3: Definition of congruent angles
R5: Definition of supplementary angles
S7: m∠1 + m∠2 = 180°
S8: ∠1 is supplementary to ∠2
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AB is a line segment.
The midpoint of the line segment AB has coordinates (3, 5)
Point A has coordinates (9, 2)
Work out the coordinates of point B.
Answers
Answer:
(-3,8)
Step-by-step explanation:
Lets say two points are (x1,y1) and (x2,y2), the midpoint will be:
((x1+x2)/2,(y1+y2)/2)
Plugging the point A in, we get: the midpoint, (3,5) as (((9+x2)/2),(2+y2)/2)
We can assign x2 and y2 as variables.
(9+x2)/2=3
9+x2=6
x2= -3
(2+y2)/2=5
2+y2=10
y2=8
therefore we get the point (-3,8)
There are better ways and this is the "formulaic (ig) way" to do this
The midpoint of a line segment means a point which lies in the mid of the given line segment. The coordinate of point B is (-3,8).
What are the coordinates of the midpoint of the line segment AB?The midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m)/2
and
y = (q+n)/2
The coordinate of the midpoint (x,y)=(3,5), while the coordinate of A(p,q)=(9,2). Thus, the coordinate of point A are,
x=(p+m)/2
3=(9+m)/2
6=9+m
m = -3
y = (q+n)/2
5 = (2+n)/2
10=2+n
n=8
Hence, the coordinate of point B is (-3,8).
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A $500 prize is shared equally between Maxwell and
Lino.
What fraction of the money does Maxwell get?
Answers
Answer:
1/2 50% $250
Step-by-step explanation:
Answer:
250$, or in fraction form, 1/2
Step-by-step explanation:
There are 2 people, so divide 1 whole by 2. Which is .5, or 1/2
Solve the following system: y = x 3 2x y = 9 (2, 5) (5, 2) (â’2, 5) (2, â’5).
Answers
The required solution of the equation is (2,5). The correct option is A. (2,5).
Given equations,[tex]y=x+3.....(1)\\2x+y=9......(2)[/tex]
How to solve a system of equations?putting the value of y from eq. 1 in eq. 2 we get,
[tex]2x+x+3=9\\3x=9-3\\3x=6\\x=2[/tex]
putting the value of x=2 in eq. 1 we get,
[tex]y=2+3\\y=5[/tex]
Hence, the required solution of the equation is (2,5).
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if the discriminant is negative how many solutions are there
Answers
Answer:
no real solutions
Step-by-step explanation:
If it is a quadratic equation, there are always two solutions, regardless of the value of the discriminant.
When the discriminant is negative there are no real solutions, but there are two complex solutions.
IF 15 CHOCOLATE COST 10 RUPEES THEN HOW MUCH DOES 1 CHOCOLATE COSTS.
Answers
Answer:
2/3 Rupees
Step-by-step explanation:
Lets say Chocolate is C and a rupee is R.
Then, 15C = 10R. We can simplify to 3C = 2R. Now we divide both sides by Three to get C = 2/3R, which means a chocolate is 2/3 of a rupee!
Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table shows the value of the cement mixer after the first and second years: Year 1 2 Value (in dollars) 47,158. 35 41,027. 76 Which function best represents the value of the cement mixer after t years? f(t) = 47,158. 35(0. 87)t f(t) = 54,205(0. 13)t f(t) = 47,158. 35(0. 13)t f(t) = 54,205(0. 87)t.
Answers
The value of cement mixer after t year is [tex]f(t) = 54,205(0. 87)^{t}[/tex]
Given to us
The value of cement mixer when bought, [tex]P[/tex]= $ 54,205
the value of cement mixer after 1 year, [tex]P_1[/tex]= $ 47,158. 35
the value of cement mixer after 2 year,[tex]P_2[/tex]= $ 41,027. 76
To find out depreciation we can use the formula for depreciation,
[tex]P_n= P(1-r)^n\\where,\\P_n= Value\ of\ asset\ after\ n\ year\\P= Value\ of\ asset\ when\ bought\\r= rate\ of\ depreciation\\n= number\ of\ years[/tex]
By putting the value, in the formula we get,
[tex]P_1= P(1-r)^n\\\\47,158.35= 54,205\times (1-r)^1\\\\\dfrac{47,158.35}{54,205} = (1-r)\\\\0.87=1-r\\\\r=0.13[/tex]
Therefore, putting the value of [tex]r[/tex] and [tex]P[/tex] in depreciation formula for [tex]t[/tex] years we get,
[tex]P_n= P(1-r)^n[/tex]
[tex]f(t) = 54,205(0. 87)^{t}[/tex]
Hence, the value of cement mixer after t year is [tex]f(t) = 54,205(0. 87)^{t}[/tex].
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14. Complete the table below to represent y = 0.25x + 3.
Then draw a graph to represent the relationship between
the x and y-values.
Answers
Answer: 3 is the y intercept; so it will touch the y axis at 3, and 0.25 is the slope of the line
Step-by-step explanation:
go to desmos. com/calculator and put that equation, if you are having a hard time visualizing it.
4x+3y = 22 (slope intercept forma
Answers
Answer:
I am pretty sure it is y=22-4x/3
Step-by-step explanation:
4x+3y=22
(you need to put it in y=mx+b format)
-subtract 4x on both sides-
3y=22-4x
-divide by 3 on both sides-
y=22-4x/3
Not sure if this is correct, but I hope this helps!
BRAINLIEST
Please answer these
Answers
Answer:
that's my answer in mathematics hope it helps for you
Find the diameter of a circle whose Circumfrence is 66 m
Answers
Answer:
21.00845
Step-by-step explanation:
πD = 66m
D = 66x 7/22
D = 21m is your answer brainlist me plz
A. Decide whether the given examples illustrate a constant or a variable.
1. Number of family members in each house
2. Amount of money in the bank every month
3. Number of seconds in a minute
4. Weekly expenses of groceries
5. Number of years in a millennium.
Asynchronous task on introduction to algebraic expressions
B. Make your own algebraic expressions based on the given conditions.
1. A variable
2. A combination of any number and any variable related by exponentiation.
3. A combination of any two variables related by subtraction.
4. A combination of any number and any three variables related by multiplication.
pls answer and help me..
Answers
Answer:
a constant is a data item whose value cannot change during the program execution just as its name implies that the value is constant a variable is a data item whose value can change during the program's execution . Thus as its name implies the the value can vary
Stacy was sitting in a seat at a football game when another ticket holder told her she was in the
wrong seat. The other ticket holder politely told Stacy she needed to go 3 rows down and 5
seats to the right. Which rule describes the translation needed to put Stacy in the correct seat?
(x, y) + (x - 5, y + 3)
(x, y) = (x - 3, y + 5)
(x, y) = (x + 5, y - 3)
(x, y) = (x + 3, y-5)
Answers
Answer:
The answer is (x, y) = (x + 3, y-5)
Step by step explanation:
So y is the up and down axis while x it the side to side axis, so for y it would be 5 down (-5) and for x it would be 3 to the right (3).
Your Welcome. :)
Isolate the variable to solve 4x + 4 > –20. Which number line shows the solution set?
HURRY!!!! I'LL GIVE YOU BRAINEIST!!
Answers
Answer:
B save your time its the same answer
Step-by-step explanation:
Good Luck!
Which is an equation of the line through the origin and (-5,6)?
A. y=-5/6x
B. y=-6x
C. y=-5x
D. y=- 6/5x
Answers
Answer:
y=-6/5x
Step-by-step explanation:
In the ratio of 3:3:2, three sisters invested a total of 54,000 pesos to a store. Find the share of the second sister in the investment.
Answers
Answer:
20, 250
Step-by-step explanation:
3:3:2
u will first need to find the addition of all the ratio and divide each ratio by the sum
3+3+2=8
the u will; 3/8×54000=20,250
3/8×54000=20,250
2/8×54000=13500
solve for x
plsss. & then solve for y
Answers
Answer:
x=22, y=35
Step-by-step explanation:
since this is an isosceles triangle, 3x-11 = 2x+11. so x=22
since this is a triangle 3x-11 + 2x+11 + 2y = 180. plug in x and simplify to get 2y+110=180, so 2y=70 and y=35
PLEASE HELP ME OUT I WILL GIVE BRAINLIEST
Metallic blocks X, Y, and Z were placed in the graduates A,B,C the initial volume of liquid in the equal sized graduates was 40 ML. Which block was placed in which graduate?
Answers
Answer:
Answers are B-Y, C-Z, A-X
Mary is 19 years younger than Jordan. Sarah is 49. Leo is 11 years younger than Sarah and 3 years
younger than Jordan. How old is Mary?
Answers
Answer:
22 years old
Step-by-step explanation:
Sarah - 49 years old
Leo - 38 years old
Mary - 22 years old
Jordan - 41 years old
I think I'm right
First person to get it right will get brainly and 20points
Answers
if i have 2 Ds and 3 Bs will i move on too 7th grade? i have one d in history and one d in language arts but Bs in evrything else
Answers
Answer:
you will bcz u didn't fail
how do you solve this question
Answers
Let the ceilings be a & b
and the distance from one corner of the ceiling to the opposite be c
then using Pythagoras theorem
[tex]c = \sqrt{a {}^{2} + b {}^{2} } \\ c = \sqrt{16 {}^{2} + 12 {}^{2} } \\ c = \sqrt{256 + 144 } \\ c = \sqrt{400} \\ c = 20[/tex]
hence ,c .°. the distance from one corner of the ceiling to the opposite is 20
Five Identical semicircles are arranged as shown.
Find the diameter of one circle
Answers
The diameter of one circle is 28 units
Find the diagram shown below:
Considering the semi-circle at the centre.
Let the unknown distance from the left be x:Let the unknown distance from the right be y:To get the value of "x"
x + 16 = 22
x = 22 - 16
x = 6
To get the value of "x"
16 +y = 22
y = 22 - 16
y = 6
Diameter of one of the circle = x + 16 + y
Diameter of one of the circle = 6 + 16 + 6
Diameter of one of the circle = 28
Hence the diameter of one circle is 28 units
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regan sold 2200 cookies in a fundraiser to "save the world" and raised $5000. If she sold
her Snickerdoodle cookies for $1.50 each and chocolate chip cookies for $4.00 each, how
many chocolate chip cookies did she sell?
Answers
Answer:
she sold 680 chocolate chip cokies
Step-by-step explanation:
pPLEASE HELP ME, I NEED HELP I CANT UNDERSTAND I COULD JUST GUESS BUT ITS IMPORTANT PLS
Answers
Answer: where’s the question??
PLEASE HELP I WILL GIVE BRAINLIEST IF YOU ARE CORRECT
Which of the following is a function equivalent to
f(x)=3(1.2)4x ?
Group of answer choices
f(x)=3(2.01)x
f(x)=3(2.07)x
f(x)=3(4.8)x
f(x)=12(1.2)x
Answers
Answer:
f(x)=12(1.2)x
Step-by-step explanation:
