given the function f(x)=-2x^4-16x^3-36x^2, determine all intervals on which f is both decreasing and concave down
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.
The weight of a beaker is measured to be 78 grams, but the actual weight of the beaker is 82 grams. What is the approximate percent error in the measurement? A) 4% B) 5% C) 6% D) 7%
The approximate percentage error on the weight of the beaker is 5%
What is percentage error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
Error = Actual value - estimated value =
Actual value = 82g, Estimated value = 78g
Error = 82 - 78 which is 4
percent error = error/estimated x 100%
percent error = 4/78 x 100 which is 5%
In conclusion the percent error is 5%
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PLEASE HELP 60 POINTS
if l || m, find the value of x
Answer:
x = 15
Step-by-step explanation:
84 = 5x + 9
Subtract 9
75 = 5x
Divide by 5
x = 15
Answer:
x = 15
Step-by-step explanation:
5x + 9 and 84 are alternate angles and are congruent , so
5x + 9 = 84 ( subtract 9 from both sides )
5x = 75 ( divide both sides by 5 )
x = 15
Which is the best example of a down payment?
A. Margo leases an apartment and pays $500 cash as a security deposit when she moves in.
B. Robby pays 10 percent cash up front and gets a loan for the
remaining 90 percent of the cost of a condominium.
C. Billy orders a piano, pays half the cost up front, and has to pay the other half when the piano is delivered.
D. Jan signs a cell phone plan that includes a little of the cost of her new phone as part of her bill every month.
The best example of a down payment is given as follows:
C. Billy orders a piano, pays half the cost up front, and has to pay the other half when the piano is delivered.
What is the down payment of a purchase?The down payment of a purchase is when a part of the purchase is paid when the purchase is made, and the other part(subjected to interest or not), is paid later.
In this problem, the example of a down payment is given by option C.
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Answer:
B. Robby pays 10 percent cash up front and gets a loan for the remaining 90 percent of the cost of a condominium
Step-by-step explanation:
i just did it
I NEED HELP FOR 3 AND 4 PLEASE I GIVE 30 POINTS.
Answer:
Number 3 is 10
Step-by-step explanation:
16+13(10)=146
14(10)+6=146
Answer:
See answer below.
Step-by-step explanation:
# 3 x = number of boxes
$16 + 13x = Tracy cost
$6 + 14x = Brendan cost
The costs are equal.
16 + 13x = 6 + 14x
10 + 13x = 14x
10 = x
#4 First plan second plan
x = number of people at a table x = number of people at a table
y = number of people at a booths y = number of people at a booths
24x + 21y = 270 multiply by 23 ⇔ 552x + 483y = 6210
14x + 23y = 222 multiply by -21 ⇔ -294x - 483y = -4662
258x = 1548
x = 6
Six people at each tables
24 (6) + 21y = 270
144 + 21y = 270
21y = 126
y = 6
Answer: 6 people at each table; 6 people at each booth.
combine over common denominator 2/3a + 1/3 - 4/a
A line passes through (2, -1) and (4, 5).
-
Which answer is the equation of the line?
-3x+y=17
-3. + 5y = -13
-3x+y=-7
-3x+5y=13
Answer:
its c
Step-by-step explanation:
Which option below is not a potential risk of purchasing a used car?
used cars can require repairs sooner
Shorter lifespans of the engine and transmission
used cars can have lower initial cost
unexpected issues may arise
Answer:
used cars can have a lower initial cost
Step-by-step explanation:
it is not a risk/hinder to purchasing a used car
I need to know this give me answer
Answer:the answer is b 10/21
Step-by-step explanation:
Answer:
B) 10/21
Step-by-step explanation:
Keep, change, flip
keep 2/7, change to multiply, flip to 5/3
2/7 x 5/3 = 10/21
Hope this helps! Pls give brainliest!
[tex]\sqrt[n]{x} \\ x^{2} \sqrt[n]{x}[/tex]Ms. Sanchez is purchasing a car for $14,000. The tax rate in the state where she is buying the car is 7%. What is the total amount she will pay for the car including the tax?
One gallon of gas costs $1.50. Three gallons of gas costs $4.50. How much will 9 gallons of gas cost?
Answer:
9 gallons will cost $13.50
Step-by-step explanation:
1 gallon = $1.50
1.50 x 9 = 13.50
or
3 gallons = $4.50
4.50 x 9 = 13.50
Answer:
13.5 dollars.
Step-by-step explanation:
4.50 times 3 is 13.5 dollars.
Have A Good Day!!! :)
Write the equation of the line in fully simplified slope-intercept form
Answer:
y = -5/6x + 6
Step-by-step explanation:
Since we have 2 points, (6,0) and (6,1), we can calculate for the slope by using the formula
Slope = m = (y2 - y1)/(x2-x1) = (1-6)/(6-0) = -5/6
Then plug in m, x(from one of the point), and y(from one of the point) to the equation y = mx + b which get us 0 = -5/6*6+b if we use the point (6,0). Now we'll get b = 6. And then plug in -5/6 for m and 6 for b into the equation y = mx + b we'll get y = -5/6x + 6
A store has 3 separate displays of color markers. There are 14 sets of color markers in each display. There are 15 markers in each set. What is the total number of markers on display?
A.) 240
B.) 630
C.) 210
D.) 633
Answer:
C.) 630
Step-by-step explanation:
14x15=210
210x3=630
See attachment for answer and math work.
Solve for y 8x - 7y = 23
[tex]8x - 7y = 23 \\ 8x - 23 = 7y \\y = \frac{8}{7} x - \frac{23}{7} [/tex]
The solution of the equation, when it is solved for y, has one variable term x with coefficient 8/7 and one constant term 23/7, 8/7x-23/7.
How to solve an equation for its variable?The solution of an equation is the value of the variable of the equation, for which the equation is satisfied.
To solve an equation for its variable, isolate the variable on one side of the equation using the mathematical operations.
The given expression is,
[tex]8x - 7y = 23[/tex]
The expression has two variables, x and y. To solve it for y, subtract 8x from both sides,
[tex]8x - 7y -8x= 23-8x\\-7y=23-8x[/tex]
Divide with number 7 both sides and change the sign of the equation,
[tex]y=-\left(\dfrac{23-8x}{7}\right)\\y=\dfrac{8x-23}{7}\\y=\dfrac{8}{7}x-\dfrac{23}{7}[/tex]
Thus, the solution of the equation, when it is solved for y, has one variable term x with coefficient 8/7 and one constant term 23/7, 8/7x-23/7.
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HELP PLEASE ANYONE
Derrick has 3 times as many CDs as Joshua. Which equation compares the number of CDs that the two boys have? (Let d = number of Derrick's CDs and j = number of Joshua's CDs.) O A. 3d = j E ов O B. 3j = d c C. 3 + d = j OD. 3 + j = d
Answer:
b
Step-by-step explanation:
joshua times 3 is basically derrick's amount
so 3j = d
Find the slope of the line.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of the line is
(Simplify your answer. Type an integer or a fraction.)
OB. The slope is undefined.
Answer:
sorry
for this answer
Labor unions arose in the nineteenth century as increasing numbers of Americans took jobs in factories, mines, and mills in the growing industrial economy.
The Knights of Labor, founded in 1869, was the first major labor organization in the United States. The Knights organized unskilled and skilled workers, campaigned for an eight hour workday, and aspired to form a cooperative society in which laborers owned the industries in which they worked.
The Knights’ membership collapsed following the 1886 Haymarket Square riot in Chicago. By 1886 the American Federation of Labor (AFL), an alliance of skilled workers’ trade unions, was growing.
For any number n>1, is
п
2 3
+ i
3
4
a. Greater than 1?
b. Less than 1?
C. Equal to 1?
A because the > symbol means greater so if n is on the open side that means its greater
~Shoto Todoroki here~
its option A
i figured this out by trial and error :/
have a good day!
HELP what is the slope
Answer:
D
Step-by-step explanation:
The line starts at 10 so I think it's that
Answer:
Slope of a line
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
m = slope
(x_1, y_1) = coordinates of first point in the line
(x_2, y_2) = coordinates of second point in the line
Step-by-step explanation:
Khan Academy
Slope review | Algebra (article) | Khan Academy
x+2y=0
3x+4y=4
find the solution
Answer:
(x, y) = (4, -2)
Step-by-step explanation:
The coefficient of y in the second equation is double the coefficient of y in the first. We can subtract twice the first equation from the second to eliminate y.
(3x +4) -2(x +2y) = (4) -2(0)
x = 4 . . . . . . . . . simplify
Substituting into the first equation, we have ...
4 +2y = 0
2 +y = 0 . . . . . . divide by 2
y = -2 . . . . . . . . subtract 2
The solution is (x, y) = (4, -2).
I NEEEEED HELP AND QUICK T~T
Answer:
5. Alt ext, 6. Alt int, 7. Alt ext, 8, SS Int, 9. Corr
Step-by-step explanation:
5. Alternate exterior since they are on opposite sides of the transversal but both are exterior to parallel lines.
6. Alternate interior, opposite sides of transversal but both are inside the parallel lines.
7. Alternate exterior, same as #1
8. Same side interior since they are on the same side of the transversal and both are inside the parallel lines
9. Corresponding since they are at the same place on the 2 parallel lines.
50 squared is rational
True
False
Answer:
false
Step-by-step explanation:
Answer:
A rational number can be written as a fraction. Try finding the square root of 50 and see if you can rewrite it in fraction form.
Step-by-step explanation:
Solve for x.
5.3>x+25
x>4910
x<5710
x<4910
x>5710
Answer:
x= < 4 9/10
Step-by-step explanation:
I hope this helps
Have a great and blessed day
Answer:
K12 Answer
Step-by-step explanation:
Jett leaves for the airport at 3:20 p.m. The airport is a 35-minute drive from his house. What time does he reach the airport?
Answer:
3:55
Step-by-step explanation:
add 35 to 20 then put the hour =
3:55
A boy stands 12 metres from the foot of the building and observes the angle of elevation of the top of the building. The height is of the building is approximately
Answer:
10.07 meters
Step-by-step explanation:
We are given that the angle of elevation is 40° and the boy is 12 meters from the building.
This means that in order to figure out the height of the building, we must use the tangent function which states that [tex]tan(\theta)=\frac{opposite}{adjacent}[/tex].
The opposite side in this case is the height of the building in relation to the angle and the adjacent side is the distance the boy is away from the building.
Therefore, we can find the height of the building by plugging in our known information and solving for the opposite side:
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
[tex]tan(40^\circ)=\frac{x}{12}[/tex]
[tex]12tan(40^\circ)=x[/tex]
[tex]x=12tan(40^\circ)[/tex]
[tex]x\approx10.07[/tex]
Therefore, the height of the building is approximately 10.07 meters.
What is an equation of a line that passes through (0,3) and (2,4)
Answer:
y=1/2x+3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-3)/(2-0)
m=1/2
y-y1=m(x-x1)
y-3=1/2(x-0)
y=1/2(x)+3
y=1/2x+3
HELPPPPPP WIL GIVE BRANELISTTTT
Answer: i think the answer is B
Step-by-step explanation:
I NEED HELP PLEASE AND THANK YOU (asap)
Which relation represents a linear function?
A) (5,6), (3,8), (1,10), (-1, 12)
B) (-3,1), -1,4), (1,9), (3,16)
C) (-2,0), (0,1), (2,3), (4,6)
D) (7,-1), (4,-3), (1,-6), (-2,-9)
Jackie likes coffee. She ________ about eight cups of coffee every day.
a-is drinking
b-drinks
c-is always drinking
d-drank
Pls help me rn bec sue tmr pls pls
Answer:
Number of 1-cm cube 24. Volume of solid 24 cm^2
Step-by-step explanation:
The sum of two numbers is 20. One number is 3 times the other number. Find the two numbers, show your work
Answer:
5 and 15
Step-by-step explanation:
20 = 3x+x
Answer: The smallest number is 20, and the largest number is 27. (27 - 20) + 1 = 8. Eight numbers make 4 pairs, and the sum of each pair is 47. 4 x 47 = 188. The sum of the numbers from 20 to 27 is 188.