Use the graph of f to estimate the local maximum and local minimum. (explain)
Answers
Answer:
The graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
Step-by-step explanation:
Consider the provided graph.
it is not always possible to find maximum or minimum for the whole function, but locally it is.
To find the local maximum and minimum we need to choose an interval first.
Local maximum: f(c) ≥ f(x) for all x in the interval
Local minimum: f(c) ≤ f(x) for all x in the interval
For better understanding refer the figure 1
Now consider the provided graph:
The graph of the function at (-2,-4) and (2,-4) shows the minimum value that is -4.
Because at x = -2 and 2 the value of function f(x)≥f(c) for every x in the domain.
Also the graph of the function has local maximum at (0,0) as at x = 0
The value of function f(x)≤f(c) for every x in the domain.
Hence, the graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
Related Questions
Jack's overtime wage is $3 per hour more than his regular hourly wage. He worked for 5 hours at his regular wage and 4 hours at the overtime wage. He earned $66. Find his regular
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The sum of two numbers is 28. one number is 14 more. find the numbers
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_______________________________________
Explanation:
_______________________________________
The numbers are: "x" and "x + 14" .
x + (x + 14) = 28 . Solve for "x" ; and then solve for "x + 14" .
_______________________________________
→ x + (x + 14) = 28 ;
Rewrite as:
→ x + x + 14 = 28 ;
→ 1x + 1x + 14 = 28 ;
→ 2x + 14 = 28 ;
Subtract "14" from each side of the equation;
→ 2x + 14 − 14 = 28 − 14 ;
→ 2x = 14 ;
Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 2x / 2 = 14 / 2 ;
→ x = 7 .
_________________________________________
So; one of the numbers is: " 7 " .
The other number is: " x + 14 " ; which equals: " 7 + 14 = 21".
The other number is: "21 " .
_________________________________________
The numbers are: "7 " and "21 " .
_________________________________________
The equation y= 3x relates the number of points resulting from three-point baskets.
What is the constant of proportionality in this equation?
A.1
B.3
C.x
D.y
Answers
y = 3x Divide both sides by x
y/x = k = 3
Thee constant of proportionality is B) 3
Answer:
3
Step-by-step explanation:
Find the equation of the line l where l is perpendicular to y=2/5x and passes through the points (5,2)
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The stores below each have the same snowboard for an original price of $189.59. At which store can you get the snowboard for the lowest price?
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Answer:
D. You can get the lowest price at Store C.
Step-by-step explanation:
Edge 2021
Arliss has two pieces of carpet runner. One is2/13 yards long and the other3/13
is yards long. She needs 10 yards of carpet runner altogether. How much more does she need to buy?
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1. Add the two given fractions.
2. Subtract the sum from 10 to find your answer.
Answer:
5 2/3
Step-by-step explanation:i thought this problem was literally impossible to do and its stopped me from progressing but i finally found out the answer and here it is
create a real world problem that represents 5/6 + 1/8.
Answers
1/8 =6/48
5/6= 40/48
so the answer is 46/48 or 23/24
hope i helped
Answer:
me and my friend are buying some pie im pay for it so i get 5/6 and he gets 1/8 how much pie did we buy
1/8 =6/48
5/6= 40/48
so the answer is 46/48 or 23/24
Step-by-step explanation:
I need help! THIS IS NOT MULTIPLE CHOICE!!!! The time needed to roast a chicken depends on its weight. Allow at least 20 min/lb for a chicken weighing as much as 6 lb. Allow at least 15 min/lb for a chicken weighing more than 6 lb. a. Write two inequalities to represent the time needed to roast a chicken. b. Graph the inequalities.
Answers
if y is the time required to cook the bird and x is number of chicken lbs
y = 20x when x ≤ 6
y = 15x when x > 6
To Graph:
Have the y-axis (minutes) go by 5's since slopes of both equations are multiples of 5. The y-axis, I would suggest go to atleast 150 minutes for a 10 lbs chicken. The x-axis is in lbs and can go by 1 lb marks.
Start with the first equation where the chicken is smaller than or equal to 6 lbs. (0,0) (1,20), (2,40) (3, 60), (4,80), (5,100) to 6lbs (6,120). If the equation is EQUAL TO the point and the line will be SOLID.
for the second equation, the chicken is larger than 6 lbs. Start with x = 6 but the point will be OPEN and the line DASHED because it's NOT EQUAL TO. (6,90) (7,105) (8,120) (9,135), (10, 150) .... and on arrow to show this
assume that y varies inversely with x. if y=27 when x=12, find x when y=-12.
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27=k/12 => k=27*12=324
so the equation is y=324/x
when y=-12, -12=324/x => x=324/(-12)=-27
What is the initial value of the exponential function shown on the graph
Answers
Answer:
The initial value of the exponential function is 2
Step-by-step explanation:
A function is a mathematical relation in which we input the values of a domain that generate the output values of a range.
Initial value of the function is the output value of the function when the input is x =0.
As shown in the graph:
The exponential function cut at the point (0, 2)
where;
y=2 when x=0.
Therefore, the initial value for the exponential as shown in the figure is, 2.
How do I write the interval(s) for which f(x) is greater than or equal to 0 (interval notation)
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-2. This could be expressed as (-infinity, -2). Also, all x values greater than 0 also lead to a y-value greater than 0. Thus, another interval would be (0, infinity). Thus, the answer is (-infinity, -2) and (0, infinity).
To write intervals where f(x) is greater than or equal to 0, solve the equation f(x) >= 0 for x. The solutions are then expressed in interval notation. For instance, x >= 3 is written as [3, infinity).
To write the interval for which f(x) is greater than or equal to 0 in interval notation, you first need to establish where the function is above or touching the x-axis. With algebraic functions, you simply solve the equation f(x) >= 0 for x to find where the function is non-negative. You then write these solutions in interval notation. For example, if your solution was x >= 3, you would write this in interval notation as [3, infinity). Also, keep in mind that round brackets ( ) are used when the number is not included in the interval while square brackets [ ] are used when the number is included.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A coat hanger is in the shape of isosceles triangle ABC shown in the figure. Sides AB and BC are congruent.
if m<BAC=22, then m<ABC= ?
Answers
m<ABC = 180 - 2(22)
m<ABC = 180 - 44
m<ABC =136
Answer: m∠ABC=136°
Step-by-step explanation:
In the given figure we have a coat hanger is in the shape of isosceles triangle ABC.
Sides AB and BC are congruent.
The isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Therefore, in ΔABC, we have
m∠BAC=m∠BCA
If m∠BAC=22°, then m∠BCA= 22°
By angle sum property , we have
m∠BAC+m∠BCA+m∠ABC=180°
⇒22°+22°+m∠ABC=180°
⇒m∠ABC+44°=180°
⇒m∠ABC=180°-44°=136°
⇒m∠ABC=136°
Therefore, If m∠BAC=22°, then m∠ABC=136°
A cyclist rides her bike at a speed of 12 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 5 minutes? Do not round your answers.
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Which table represents a linear function?
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Hope this helps! :)
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh 68.7 cm2 161.7 cm2 381.3 cm2 450.0 cm2
Answers
Answer:
Option B is the correct answer.
Step-by-step explanation:
We have one side = 27.6 cm
Hypotenuse = 30 cm
Length of remaining side [tex]=\sqrt{30^2-27.6^2}=11.76cm[/tex]
Area of right angled triangle [tex]=\frac{1}{2}\times \texttt{Product of lengths of 2 sides other than hypotenuse}[/tex]
Area [tex]=\frac{1}{2}\times 27.6\times 11.76=161.7cm^2[/tex]
Option B is the correct answer.
Julio's father is 4 times as old as Julio. The sum of their ages is no less than 55.
What is the youngest age Julio can be?
Enter your answer in the box.
years
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f = 4j, j+f = 55, j + 4j = 55, 5j = 55, j = 11
So youngest Julio can be is 11 years old.
Six times the sum of a number and 9 equals 8
Write in equation
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Solve.
6(x+9) = 8
6x + 54 = 8
-54 -54
6x = -46
/6 /6
x = -7.66666667
The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
A) The function has one imaginary zero.
B) The function has one real zero and two imaginary zeros.
C) The function has one real zero and one imaginary zero.
D) The function has one imaginary zero and two real zeros.
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Your polynomial has real coefficients and is of degree 3.
It can have 0 complex roots, or it can have 2 complex roots.
It cannot have only 1 complex root.
The correct answer is
D) The function has one imaginary zero and two real zeros.
x = 3, 4i, -4i
What is the value of the expression? ( 5/2 ) ^2 +3/4 ^3
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5/2 ^2 = 6 1/4 = 6.25
3/4^3 = 27/64 = 0.4201875
6 1/4 + 27/64 = 6 43/64 (mixed number)
6.25 +0.421875 = 6.671875 (decimal)
not sure what format you need, since the question was in fraction form, I think you need to answer using a mixed number though.
A rectangle is 3 units wide and 4 units long. How long is its diagonal
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x^2 = 3^2 + 4^2 = 25
x = sqrt25 = 5
Diagonal is 5 units long
Suppose g(x) = f(x + 2) – 3. Which statement best compares the graph of g(x) with the graph of f(x)?
Answers
Answer:
B. the graph of g(x) is shifted 2 units right and 3 units up
Step-by-step explanation:
just got it right
We conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. Option D is the correct answer.
The given function is g(x) = f(x + 2) – 3.
What is a function?A function is a relation for which each value from the set of the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
To shift a function right:
Subtract inside the function's argument. For example, f(x)-b is basically f(x) shifted b units to the right.
Subtracting inside the function's argument moves you to the right.
So, g(x) = f(x – 2) means f(x) is shifted two units to the right.
To move a function down:
Subtract outside the function. For example, f(x)-b is basically f(x) moved down 3 units.
So, g(x) = f(x – 2) + 3 means, f(x) is moved 3 units down.
Therefore, we conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. So, option D is the correct answer.
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Power Glen Elementary School has a plant sale to raise money for a local charity. Each plant costs 3$. It is sold for $10 a) What would be the output if the sold these many plants 10,20,30,40,50 b)How many plants have to be sold to collect $500 c) How many plants have to be sold to be able to give the charity $500?
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Choose the product. 4p^3 3(p 2^ + 8p - 3)
4p^5 + 12p^4 + 7p^3
4p^6 + 44p^3
4p^3 - 12p^2 +32p^4
4p^5 + 32p^4 -12p^3
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I hope this helps.
Answer: The correct option is
(D) [tex]4p^5+32p^4-12p^3.[/tex]
Step-by-step explanation: We are given to choose the correct expression for the following product :
[tex]P=4p^3(p^2+8p-3)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the above product, we need to multiply 4p³ with every term within the bracket.
The required product (i) is
[tex]P\\\\=4p^3(p^2+8p-3)\\\\=4p^{3+2}+32p^{3+1}-12p^3\\\\=4p^5+32p^4-12p^3.[/tex]
Thus, the required product is [tex]4p^5+32p^4-12p^3.[/tex]
Option (D) is CORRECT.
Write a number that is greater than 1 in scientific notation. explain how you know it is greater than 1
Answers
The positive power of 10 shows that the number is greater than 1.
What is scientific notation?A given number, equation, or expression is written in a format known as a scientific notation, which adheres to a set of principles. Large numbers like 8.6 billion are difficult to write in their numerical form since they are not only unclear but also time-consuming, and there is a potential that we may write a few zeros more or less.
Given:
number that is greater than 1 in scientific notation.
So, to get know the number is greater than 1 we can tell it by seeing the power of 10.
If the powers of 10 is positive then the number is also greater than 10.
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The sum of two integers is 9 their difference is 5 what are the two integers
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solve for x
x-y=5 so substitute x by 9-y
9-y-y=5
9-2y=5 isolate
9-2y-9=5-9
-2y=-4 divide both sides by -2
-2y/-2=-4/-2
y=2 and x=9-2=7
check for x+y=9
7+2=9
check for x-y=5
7-2=5 so x=7 and y=2
The values of the two integers are 7 and 2 respectively.
Let the two integers be a and b respectively.In this exercise, you're required to determine two integers from the given word problem.
Thus, we would write a mathematical (algebraic expression) for the sentence.
Translating the word problem into an algebraic expression, we have;
The sum of two integers is 9;
[tex]a + b =9[/tex] ....equation 1.
The difference between the two integers is 5;
[tex]a - b = 5[/tex] equation 2.
Solving the systems of linear equations by using the elimination method, we have:
[tex]2a = 14[/tex]
Dividing both sides by 2, we have:
[tex]a = \frac{14}{2}[/tex]
a = 7
To find the value of y:
[tex]a + b =9\\\\7 +b=9\\\\b =9-7[/tex]
b = 2
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A building that is 15 meters tall casts a shadow that is 6 meters long. at the same time, a tree casts a shadow that is 9 meters long. how tall is the tree
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Final answer:
To determine the height of the tree, we use proportions based on the shadow lengths. Since the building is 15 meters tall with a 6-meter shadow and the tree's shadow is 9 meters, the height of the tree is found to be 22.5 meters.
Explanation:
You're asking how to find the height of a tree based on its shadow's length using similar triangles. The building is 15 meters tall and casts a 6-meter-long shadow. We can set up a proportion since the tree and the building have the same sun angle, thus their heights and shadows are in proportion. We will compare the building's height to its shadow, and then set this ratio equal to the tree's height to its shadow.
Using the formula for proportions:
Building height / Building shadow = Tree height / Tree shadow
Which translates to:
15 meters / 6 meters = Tree height / 9 meters
Now we solve for the Tree height:
Tree height = (15 meters / 6 meters) * 9 meters = 22.5 meters
The height of the tree is 22.5 meters.
How can you find a unit rate when given a rate?
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Hope this helped :)
To rent a certain meeting room, a college charges a reservation fee of $37 and an additional fee of $6.70 per hour. the chemistry club wants to spend less than $90.60 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use t for the number of hours the meeting room is rented, and solve your inequality for t .
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6.70t < 90.60 - 37
6.70t < 53.6
t < 53.6 / 6.70
t < 8 <=== they could rent the meeting room for less then 8 hrs
A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
Answers
Dish B has n₂ = 6.25 x 10¹⁵ bacteria.
Calculate n₁/n₂.
[tex] \frac{n_{1}}{n_{2}} = \frac{1.75 \times 10^{18}}{6.25 \times 10^{15}} =0.28 \times 10^{18-15} = 0.28 \times 10^{3} =2.8 \times 10^{2}[/tex]
The number of times that the number of bacteria in dish A is greater than the number of bacteria in dish B is 2.8 x 10² in standard notation.
Answer: 2.8 x 10²
Write a conditional statement. Write the converse, inverse and contrapositve for your statement and determine the truth value of each. If a statement’s truth value is false, give a counterexample.
Answers
Converse If you live in Texas, then you live in Plano. False. could be Austin
Inverse If you don't live in Plano then you don't live in Texas.. False
Contrapositive If you don't live in Texas then you don't live in Plano. True