graph h(x)=x^4-3x^2+x. identity the x intercepts and the points where the local maximum and local minimum occur. determine the intervals for which the function is increasing or decreasing.Round to the nearest hundredth if necessary
Answers
I hope this helps you. Give a like
The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.
The local minimum is 1.
The function is increasing at the interval (-1.5, 0.5) and (1, ∞).
The function is decreasing at the interval (∞, -1) and (0, 1.5).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
h(x) = [tex]x^4[/tex] - 3x² + x
The x-intercept is when h(x) = 0.
0 = [tex]x^4[/tex] - 3x² + x
From the graph, we see that,
The x-intercept are at x = 0, x = -1.9, x = 0.35, and x = 1.5
Now,
h(x) = [tex]x^4[/tex] - 3x² + x
h'(x) = 4x³ - 6x
h''(x) = 12x² - 6 (positive)
So,
h(x) has a minimum value.
h'(x) = 0
4x³ - 6x = 0
4x³ = 6x
4x² = 6
x² = 6/4
x² = 3/2
x² = 1.5
x = ±√1.5
x = ±1.22
The minimum values are:
h(1.22) = [tex]x^4[/tex] - 3x² + x = -1
h(-1.22) = [tex]x^4[/tex] - 3x² + x = 1
The local minimum is 1.
From the graph, we see that,
The function is increasing at the interval (-1.5, 0.5) and (1, ∞).
The function is decreasing at the interval (∞, -1) and (0, 1.5).
Thus,
The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.
The local minimum is 1.
Increasing intervals are (-1.5, 0.5) and (1, ∞).
Decreasing intervals are (∞, -1) and (0, 1.5).
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Related Questions
In a quadrilateral ABCD, line AC = x + 6 and line BD = 2x-4. For what value of x Is ABCD a rectangle?
Answers
Answer:
x = 10
Step-by-step explanation:
The diagonals of a rectangle are the same length. This means ...
AC = BD
x +6 = 2x -4
10 = x . . . . . . . . add 4-x to both sides
The figure is a rectangle for x=10.
In football, a gain is when a player moves the ball closer to the goal line; whereas, a loss is when the player loses yardage making it difficult to score. Larry plays quarterback for the Eagles. During the team's opening football game, the Eagles have the ball 48 yards away from the goal line. On the first play, the Eagles gain 31 yards on a pass toward the goal line. On the next four plays, the Eagles lose 3, 5, 7, and 4 yards, respectively. What is the distance between the ball and the goal line after these five plays?
Answers
Answer:
36 yards
Step-by-step explanation:
48 - 31 = 17
17 + 3 + 5 + 7 + 4 = 36
The total distance between the ball and the goal line is 36 yards
What is data?In computing, data is information that has been translated into a form that is efficient for movement or processing.
Given:
Eagles have the ball 48 yards away from the goal line.
On the first play, the Eagles gain 31 yards on a pass toward the goal line. On the next four plays, the Eagles lose 3, 5, 7, and 4 yards.
After first day they have yards remaining
=48 - 31
= 17
Now, the total distance between the ball and the goal line
=17 + 3 + 5 + 7 + 4
= 36
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A square coffe shop has sides that are 7 meters long what is the coffe shops area
Answers
Answer:
49 square metres
Step-by-step explanation:
The area of a square is the length of the side times itself.
The area is 7 x 7 = 49
Plz Help....(MATH)......
Answers
Answer:
2 [tex]\frac{6}{7}[/tex]
Step-by-step explanation:
20 lbs distributed throught 7 days is [tex]\frac{20}{7}[/tex] which simplifies to 2 [tex]\frac{6}{7}[/tex]
OK im confused for real: ok so what does 20X80X100X70X40+4=
Answers
Answer:
448000004.
Hope that helps. x
Answer:
448000004
Step-by-step explanation:
QUICK MATHS
The table below gives selected values for the differentiable and decreasing function f and it’s derivative. If f^-1(x), what is the value of g’(9)
Answers
According to the table, f(x) = 9 when x = -5. So if g(x) is the inverse of f(x), it follows that g(9) = -5.
By the inverse function theorem,
[tex]g'(9) = \dfrac1{f'(g(9))} = \dfrac1{f'(-5)} = \boxed{-\dfrac14}[/tex]
what is x/-4 = -20 how do i sole for x
Answers
Answer:
x = 80
Step-by-step explanation:
Reverse your division by using multiplication:
x/-4 = -20
-4 x -20 = 80
Help!! Ill give 100 points!
Answers
It is the 3rd one from the top
Answer:
I believe the answer would be C.
Step-by-step explanation:
First of all, the solution to the answer really is 1/20. If you figure out the decimal form of 4/5, it is 0.80, which is closer to 1 than to 1/2 and 0. The decimal form of 3/4 is 0.75, which is equally close to 1 and 1/2, being 0.25 from both. But it is closer to 1 than 0. I hope I’m right, and I hope this helps. :)
If a person tells you she is 6 feet tall, is she basing that measurement on customary units or metric units?
Answers
Answer:
Customary
Step-by-step explanation:
Answer:
it is based on customary units
–7(2.3y − 2) simplified
Answers
Answer:
-16.1y + 14
Step-by-step explanation:
–7(2.3y − 2)
=> -16.1y + 14
Therefore, -16.1y + 14 is the simplified form.
Hoped this helped
[tex]GeniusUser[/tex]
Answer:
53
Step-by-step explanation:
sorry if im incorrect
Slow and steady wins the race. The leatherback sea turtle is the fastest known reptile, with a maximum speed of 21.92 21.9221, point, 92 miles per hour ( mph ) (mph)left parenthesis, start text, m, p, h, end text, right parenthesis. Which of the following equations, where d dd is distance in miles and t tt is time in hours, represents a speed that is less than that of the leatherback sea turtle?
Answers
Answer:
ang hirap naman plss answeer
HELP ME PLEASEEE !!
DON'T GIVE ME IRRELEVANT ANSWERS PLEASE
Answers
Which equation equals to 105
34+12*74=
12+1*56=
88+66-49=
34+61-7=
157-43+900
(Need an image if it’s gonna work!)
Answers
So the answer to this is C, cause I did an image
2.87x7.8
need answer
Answers
= 22.386
Hope this helps!
2.87 * 7.8
= 22.386
What is the area of 30x40 rectangle in square units?? Will give BRAINLIEST if only correct!!!
Answers
Answer:
1200 units 30 times 40 is 1200
1200 sq units
hope this helps
What is the answer to this?
Answers
Answer:
56
Step-by-step explanation:
Answer:
i think its 140 because u got to add all the sides in order to subtract from 180
i dont know if its right but that is what i think UwU
Can somebody please help me i need this urgently.
Answers
Answer:
multiple choice is worth 2
short response is worth 4
Step-by-step explanation:
23x + 10y = 86
28x + 5y = 76
solve by elimination
multiply the top by -1 and the bottom by 2
-23x + -10y = -86
56x + 10y = 152
add them
33x = 66
x = 2
with x = 2 plug x into one of the equations
23x + 10y = 86
23(2) + 10y = 86
46 + 10y = 86
10y = 40
y = 4
x = 2 and y = 4 so
multiple choice is worth 2
short response is worth 4
Please help me with this, I need a real answer quickly before the period ends. Explanation if you can too pls
Answers
Answer:
(4, -6)
Step-by-step explanation:
The rule for rotation around the origin 90 degrees clockwise is
Ro, 90: (x, y) --> (y, -x)
so (6, 4) --> (4, -6)
If 3 cans of beans cost 90¢, how many can you buy for $2.70?
If you can buy 10 juice packs for
$3.00, how much will you spend to
buy 4 juice packs?
Answers
WILL GIVE BRAINLIEST
Answers
Answer:
31). (0,-2), (2,-5).
32). (0,-1), (5,3).
33). (0,1), (5,-2).
34). (0,1), (4,0).
please explain for brainlist
A town has approximately 1000 homes. The town council is considering plans for future development. Plan A calls for an increase of 200 homes per year. Plan B calls for a 10% increase each year. Write a function to model each plan and determine the number of homes each plan has after 3 years.
Answers
Answer:
Plan A: 1600 homes after 3 years Plan B: 1330 homes after 3 years
Step-by-step explanation:
Plan A.
200x3=600
1000+600=1600
1600 homes after 3 years
Plan B.
10% the first year =100 homes increased
10% the secound year = 110 homes increased
10% the third year = 121 homes increased
1330 homes after 3 years
It would be 1330 for plan B. And plan a 1600.
hi hope you are well can someone give the answers will mark as brainliest as soon as I am done with this assignment
Answers
Answer:
41) 10
42) 65
43) 26
44) 33
45)65
41.)10
42.) 65
43.)26
44.)33
45.)65
hoped that helped:)
Using the graph below what would the y value (range) be for an x value (domain) of -1
Answers
Answer:
y = - 5
Step-by-step explanation:
locate x = - 1 on the x- axis, go vertically down to meet the line at (- 1, - 5 )
Then when x = - 1 the value of y = - 5
If you buy a stock originally valued at $2,500 then sell that stock later at $2,550 what is the percent of increase in the stock?
Answers
Answer:
2550-2500 = 5025% percent increase.
Step-by-step explanation:
Answer: 2%
Step-by-step explanation:
2500 X 1.02 = 2,550
Which of the following is a true statement of the figure?
Answers
Answer:
1st one is correct
Step-by-step explanation:
please mark my answer in brainlist plz
A store owner wishes to make a new tea with a unique flavor by mixing black tea and oolong tea. If he has 35 pounds of oolong tea that sells for $2.40 per pound, how much black tea worth $1.80
Answers
The cost of 35 pounds of oolong tea is $84.
An equation is used to show the relationship between two or more variables or numbers.
Given that oolong tea sells for $2.40 per pound.
There are 35 pounds of oolong tea available. Hence:
Cost of 35 pounds of oolong tea = $2.40 per pound * 35 pound
Cost = $84
Hence, the cost of 35 pounds of oolong tea is $84.
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Answer:
35 LB (THIS IS ACTUALLY CORRECT)
Step-by-step explanation:
First, you lay it down like this:
Since you're selling 35 pounds of oolong tea that sells for $2.40, you multiply both
2.4*35
=84
However, since you don't know how many pounds of black tea, you use x
Multiply like above
1.8*x
=1.8x
The total mixture is selling for $2.10
Total pounds: 35 + x (given above, or black + oolong tea
equation:
84 + 1.8x = 2.1(35+x)
84 + 1.8x = 73.5 + 2.1x (distributive property)
- 1.8x - 1.8x
84 + 0 = 73.5 + 0.3x
-73.5 -73.5
10.5 = 0.3x
3.5 = 0.1x
35 = x
James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,000 for their reception. If the reception hall charges a $80 cleanup fee plus $33 per person, find the
greatest number of people that they may invite and still stay within their budget.
James and Bethany can invite at most people to the reception
(Round down to the nearest whole person)
Answers
Answer:
88 people
Step-by-step explanation:
Start with the equation of
[tex]3,000\geq 33x+80[/tex]
subtract 80
[tex]3.000\geq 33x[/tex]
then divide by 33
[tex]88.48\geq x[/tex]
round down
[tex]x=88[/tex]
I need help and I can’t find any sadly. Help!!
Answers
1 = Given
2 = Addition Property of Equality
3 = Division Property of Equality
-9y + 4x - 20 = 0
-7y + 16 - 80
Answers
Answer:
Step-by-step explanation:
PLS ANSWER AS SOON AS POSSIBLE
PLSSSS
Answers
Step-by-step explanation:
<B=180°-70°-50°=60°
hope this helps you.