Find the absolute maximum and absolute minimum values of f on the given interval.

f(x) = xe^−x^2/32, [−2, 8]

Answers

Answer 1

The question is missing parts. Here is the complete question.

Find the absolute maximum and absolute minimum values of f on the given interval.

[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex] , [ -2,8]

Answer: Absolute maximum: f(4) = 2.42;

              Absolute minimum: f(-2) = -1.76;

Step-by-step explanation: Some functions have absolute extrema: maxima and/or minima.

Absolute maximum is a point where the function has its greatest possible value.

Absolute minimum is a point where the function has its least possible value.

The method for finding absolute extrema points is

1) Derivate the function;

2) Find the values of x that makes f'(x) = 0;

3) Using the interval boundary values and the x found above, determine the function value of each of those points;

4) The highest value is maximum, while the lowest value is minimum;

For the function given, absolute maximum and minimum points are:

[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex]

Using the product rule, first derivative will be:

[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex]

[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex] = 0

[tex]1-\frac{x^{2}}{16}=0[/tex]

[tex]\frac{x^{2}}{16}=1[/tex]

[tex]x^{2}=16[/tex]

x = ±4

x can't be -4 because it is not in the interval [-2,8].

[tex]f(-2)=-2e^{-\frac{(-2)^{2}}{32} }=-1.76[/tex]

[tex]f(4)=4e^{-\frac{4^{2}}{32} }=2.42[/tex]

[tex]f(8)=8e^{-\frac{8^{2}}{32} }=1.08[/tex]

Analysing each f(x), we noted when x = -2, f(-2) is minimum and when x = 4, f(4) is maximum.

Therefore, absolute maximum is f(4) = 2.42 and

absolute minimum is f(-2) = -1.76

Answer 2

The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

The function is given as:

[tex]\mathbf{f(x) = xe^{-\frac{x^2}{32}}}[/tex]

Start by differentiating the function

[tex]\mathbf{f'(x) = e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}}}[/tex]

Set to 0

[tex]\mathbf{ e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}} = 0}[/tex]

Rewrite as:

[tex]\mathbf{ \frac{x^2}{16}e^{-\frac{x^2}{32}} = e^{-\frac{x^2}{32}}}[/tex]

Cancel out common factors

[tex]\mathbf{ \frac{x^2}{16}=1}[/tex]

Multiply both sides by 16

[tex]\mathbf{ x^2=16}[/tex]

Take square roots of both sides

[tex]\mathbf{ x=\pm 4}[/tex]

The interval is given as: [-2,8]

This means that the value of x = -4, is out of the interval.

So, we have the following critical points:

x = (-2, 4, 8)

Calculate f(x) at the these points

[tex]\mathbf{f(-2) = -2 \times e^{-\frac{(-2)^2}{32}}}[/tex]

[tex]\mathbf{f(-2) = -2 \times e^{-\frac{4}{32}}}[/tex]

[tex]\mathbf{f(-2) = -1.765}[/tex]

[tex]\mathbf{f(4) = 4 \times e^{-\frac{(4)^2}{32}}}[/tex]

[tex]\mathbf{f(4) = 4 \times e^{-\frac{16}{32}}}[/tex]

[tex]\mathbf{f(4) = 2.426}[/tex]

[tex]\mathbf{f(8) = 8 \times e^{-\frac{(8)^2}{32}}}[/tex]

[tex]\mathbf{f(8) = 8 \times e^{-\frac{64}{32}}}[/tex]

[tex]\mathbf{f(8) = 1.083}[/tex]

By comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

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Related Questions

idk what this answer would be help please!

Answers

They will save $6.

Explanation:

For Science center, 1 ticket = $36.75/3 = $12.25
i)So for 12 tickets = $12.25 X 12 = $147

For zoo, 1 ticket = $51/4 = $12.75
ii) So for 12 tickets = $153

Difference of i and ii,
$153-$147 = $6

So, they will save $6 by choosing science center.


Hope thus helps:)

fill in the blanks polynomials​

Answers

Step-by-step explanation:

2 degrees

1 terms..

hope it helps you...

take care buddy....

which of the following expression eqaul to -4x^2-36

Answers

-4(x^2+9) is what I got.

Answer:

2hole square and six whole square (a+b) (a-b) finish...

Supervisor: "I see that 1000 calls were sent to your extension this month. 15% of those calls were not answered, which means that you did not answer __________ calls this month."

Answers

Step-by-step explanation:

850 calls

1000:100=10

1%=10

10×85=850

Discount is the reduction in value. The total number of calls not answered this is 150 calls

Discount and percentages

Given the following

Total number of calls = 1000 calls

If 15% of those calls were not answered, the total calls that were not answered is given as:

Total call not answered . = 0.15 * 1000

Total call not answered = 150 calls

Hence the total number of calls not answered this is 150 calls

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98.643 ÷ 0.04
Round your answer to the nearest hundredth.

Answers

Answer:

7466.07

Step-by-step explanation:

Find the number in the hundredth place and look one place to the right for the rounding digit . Round up if this number is greater than or equal to and round down if it is less than.

btw you should try out

Ms. Rogers asked 15 piano students how many hours of practice they put in each week. The list shows the data she recorded.

6,6,7,7,7,8,8,8,8,8,9,9,9,10,10

Which statement is true?

A.The data is skewed to the left.
B. The data is skewed to the right.
C. The data is symmetrical.
D. The skew of the data cannot be determined.

Answers

Answer:

D

Step-by-step explanation:

A student that goes to class can not put 10 hours of practice per day.

Answer:

The data is skewed to the left.

Step-by-step explanation:

Please help me on this question

Answers

Answer:

B

Step-by-step explanation:

Write a word expression for 7 + 4a.

Answers

Answer:

The answer is Seven plus Four A.

if k = am+3mx what is the value of m in terms of
x
Please help

Answers

Answer:

k = am + 3mx

Group by taking common factor m

k = m(a + 3x)

Divide both sides by (a +3x)

k / (a+3x) = m

Then, m = k / (a+3x). This is the answer

Step-by-step explanation:

Using the diagram, find the measure of the angle indicated in bold.

A 95
B 110
C 120
D 130

Answers

I believe it would be C not 100% sure but hope this helped! :)

Find the line's slope and a point on the line. y-2=1/3(x+4)
slope:
point on the line: ​

Answers

Format: y - y1 = m(x - x1)
m is slope
answer: slope: 1/3
Point on the line: (-4, 2)

JANITIA IS 15 YEARS OLD AND HER BROTHER IS 5 YEARS. WHAT IS THE RATIO OF JANTIA AGE TO HER BROTHER AGE

PLEASE ANSWER MY QUESTION

Answers

Answer:

3:1

Step-by-step explanation:

15:5 = 3:1

Answer:

3:1

Step-by-step explanation:

15:5

3:1

i think this is the answer

plz i need help with this

Answers

Answer:

congruence, corresponding,sum of 180

Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is One-half. What is the probability that the next child born to the same familiy will also be a girl?
a.
One-half
b.
One-fourth
c.
StartFraction 1 Over 8 EndFraction
d.
StartFraction 1 Over 12 EndFraction

Answers

I’d say A. one half! hope it helped! not 100% sure

Answer:

B

Step-by-step explanation:

EDG2021

We know that 65% of all Americans prefer chocolate over vanilla ice cream. Suppose that 1000 people were randomly selected. What is the standard error of the sample proportion

Answers

its not 65% americans like all

The standard error of the sample proportion is 0.0002275

What is the standard error of the sample proportion?

The standard error of a proportion p in a sample of size n is given by:

[tex]S= \sqrt{\frac{p(1-p)}{n}}[/tex]

Now it is given that,

Number of people selected is 1000.

So, sample size, n 1000

Americans prefer chocolate = 65%

Thus, proportion, p = 0.65

So, standard error of a proportion is given as,

[tex]S= \sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]S= \sqrt{\frac{0.65(1-0.65)}{1000}}[/tex]

[tex]S= \sqrt{\frac{0.65(0.35)}{1000}}[/tex]

[tex]S= \sqrt{\frac{0.2275}{1000}}[/tex]

[tex]S= 0.0002275[/tex]

this is the required standard error of the sample proportion.

Thus, the standard error of the sample proportion is 0.0002275.

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Students in Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.8. They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. What is the probability that the students will have their homework checked and take a pop quiz on a randomly chosen day?

0.48
0.54
0.72
0.80

Answers

Answer:

A) 0.48

Step-by-step explanation:

The probability that Mrs. Barnes does not check homework if the students take a pop quiz will be 0.77.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42.

They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9.

Then the probability that Mrs. Barnes does not check homework if the students take a pop quiz will be =

P = 0.42 x 0.6 + 0.58 x 0.9

P = 0.252 + 0.522

P = 0.774 ≈ 0.77

More about the probability link is given below.

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4x + 16 factor out gcf

Answers

Answer:

4(x+4)

Step-by-step explanation:

To factor out the gcf we need to find the greatest common factor. Then we multiply it be the other divided part.

Substance X is found in the bloodstream of humans. A random sample of 75 males had a mean content of 28 ppm of Substance X in their blood. A random sample of 50 females had a mean content of 33 ppm of Substance X in their blood. The population standard deviations for males and females are known to be 14.1 ppm and 9.5 ppm, respectively. Use the 88.12% degree of confidence. An appropriate set of null and alternative hypotheses to test whether males and females have the same amount of Substance X in their blood is:

Answers

Answer:

H0: u1 - u2 = 0

H1: u1 - u2 ≠ 0

Step-by-step explanation:

This question requires us to state the hypothesis to be used for this test to know if males and females have the same amount of substance X. I have gone further to also calculate the test statistics too.

Null hypothesis:

H0: u1 - u2 = 0

Alternative hypothesis:

H1: u1 - u2 ≠ 0

X1 = 28, sd1 = 14.1, n1 = 75

X2 = 33, sd2 = 9.5, n2 = 50

We have a 2 tailed test

Alpha = 1-0.8812

= 0.1188

Critical value = 1.56

If z<-1.56 or z>1.56

Reject null hypothesis

Test statistic

= (28-33)/14.1²/75 + 9.5²/50

= -2.37

Therefore we reject the H0 because -2.37 is less than -1.56

2/3 + 3/4
but i need to find a common denominator

Answers

Answer:

46

Step-by-step explanation:

the common one is 2

Answer:

2/3 plus 3/4 is 17/12.

Step-by-step explanation:

this is because the common denominator is 12, and once you add it all you get 17/12 :))

what is 6x+2y=18 in intercept form?

Answers

Answer:

y = -3x + 9

Step-by-step explanation:

6x + 2y = 18

move 6x to the right of the equation by subtracting on both sides

2y = -6x + 18

then to single out the 'y' divide by 2 on both sides

y = -3x = 9

 Hope this helps <3

helpppppp now plssss​

Answers

Answer:

translation of four units up

Step-by-step explanation:

Answer:

A. translation of 4 units up

Step-by-step explanation:

Take one point from each line, for example:

f(x): (0, 1)g(x): (0, 5)

The y-values of these points are 5 points apart, therefore, f(x) was translated 4 units up to get g(x).

31x m=217 what does the m mean i cant seem to figure that out.

Answers

Answer:

7?

Step-by-step explanation:

31xm=217

m=217/31

m=7

Which expression is equivalent to 6(2x + 4)?
A) 12 + 24
B) 12x + 4
C 12x + 24
D) 8x + 10

Answers

i think the answer is c

Please anerw the pic attached below!

Answers

Answer:

x = 27

Step-by-step explanation:

m<X + m<XWY + m<XYW = 180    (measures of <s of triangle add to 180)

m<X = 90

90 + m<XWY + m<XYW = 180

m<XWY + m<XYW = 90     Equation 1

m<XWY + m<VWY = 180      (linear pair)     Eq. 2

m<XYW + m<ZYW = 180      (linear pair)     Eq. 3

Add Eqs 2 & 3

m<XWY + m<VWY + m<XYW + m<ZYW = 360

m<XWY + m<VWY + m<XYW + m<ZYW = 360

According to Eq. 1, m<XWY + m<XYW = 90.

90 + m<XYW + m<ZYW = 360

Also, m<VWY = 6x & m<ZYW = 4x

90 + 6x + 4x = 360

10x = 270

x = 27

Calculate the mean, median, mode, and midrange of this quiz distribution and explain whether the distribution is skewed to the left or to the right.
a.
Mean = 9, median = 8.2, mode = 7, midrange = 9; skewed to the left.
b.
Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the left.
c.
Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the right.
d.
Mean = 9, median = 8.2, mode = 7, midrange = 9; skewed to the right.

Answers

Answer:

B

Step-by-step explanation:

Find the area of the curve y= f(x) = x between x = 5 and x = 10

Answers

Answer:

the area of the curve y= f(x) = x between x = 5 and x = 10

[tex]A=\frac{75}{2}[/tex]

Step-by-step explanation:

Finding the area of the curve  y = f(x) = x between x = 5 and x = 10

Using the Area formula

[tex]A=\int _a^b\:f\left(x\right)dx[/tex]

As the area of curve lies between x = 5 and x = 10

so

a = 5, b = 10

so the integral expression becomes

[tex]A=\int _5^{10}xdx[/tex]

[tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]

[tex]A=\left[\frac{x^{1+1}}{1+1}\right]^{10}_5[/tex]

    [tex]=\left[\frac{x^2}{2}\right]^{10}_5[/tex]

     [tex]=\frac{1}{2}\left[10^2-5^2\right][/tex]

     [tex]=\frac{1}{2}\cdot \:75[/tex]

     [tex]=\frac{75}{2}[/tex]

Therefore, area of the curve y= f(x) = x between x = 5 and x = 10

[tex]A=\frac{75}{2}[/tex]

What is the value of x? enter your answer in the box.

Answers

Answer:

X = 20

Step-by-step explanation:

3x + 50 = 6x -10

3x - 6x = -10 - 50

-3x = -60

x = -60/-3

x = 20

Answer:

x = 20

Step-by-step explanation:

Vertically opposite angles are congruent.

6x - 10 = 3x + 50

       6x = 3x + 50 + 10

       6x = 3x + 60

6x - 3x = 60

        3x = 60

          x = 60/3

x = 20

Work out the percentage change to 2 decimal places when a price of £12 is increased to £15.99.

Answers

Answer:

2/15.99 = 0.34 euros is the right answer.

write a definition for a unite rate

Answers

A unit rate is a special type of ratio (also called a single-unit rate). It will compare 1 unit of some quantity to a different number of units of a different quantity. Any ratio that is not a unit rate can be turned into one.

Answer:

Step-by-step explanation:

I wish I knew

Malloy had some money to give to his five
children. He first took $5 for himself and then
evenly divided the rest among his children.
Each child received S3 How much money did
he start with?

Answers

Answer:

$20

Step-by-step explanation:

he gave 5*3=15 dollars to his children

he took 5

add together to get 20

Answer:

$20

Step-by-step explanation:

$3 x 5 = $15

$15 + $5 = $20

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