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.

Read more about absolute maximum and absolute minimum values at:

https://brainly.com/question/12752779


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90

Step-by-step explanation:

90

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Answers

Answer:

[tex]\dfrac{5}{6}[/tex]

Step-by-step explanation:

The problem says Two-thirds divided by StartFraction 4 Over 5 EndFraction.

Two thirds means = 2/3

It means,

[tex]x=\dfrac{2}{3}\ \text{divided by}\ \dfrac{4}{5}[/tex]

or

[tex]x=\dfrac{\dfrac{2}{3}}{\dfrac{4}{5}}\\\\=\dfrac{2}{3}\times \dfrac{5}{4}\\\\=\dfrac{5}{6}[/tex]

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Answer:

30= 20 so, that’s 10 dollars of

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Step-by-step explanation:

I took the test hope this helps

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Answer:

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Answers

Answer:

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Step-by-step explanation:

We kind of have to work backward.

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Our new equation is now, 3x=15

We now take:

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Answer:

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Step-by-step explanation:

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I think it’s the 3 I’m not sure

Lin Ying belongs to an athletic club. In 800 m races her times are normally distributed with mean 128 seconds and standard deviation
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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Hope that help.

Answer:

Step-by-step explanation:

here you go mate'

step 1

-4x+3y=-2,y=x-1  equation

step 2

y=x-1;-4x+3y=-2  rewrite the equation

step 3

y=x-1  1st equation

step 4

-4x+3y=-2  saubstitute

-4x+3(x-1)=-2

-x-3=-2

step 5

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-x=1

step 6

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second equation

step 1

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y=-1-1

step 2

y=-1-1 simplify

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answer

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a

Step-by-step explanation:

because I said it was jejwjwjeiejehxueh ed uejrhcu

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580

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

From the question it self we know that 1 pound of chicken costs $3.75. In order to solve this question we just need to find out how much 1 pound does fit into 2.25 pounds and then multiple the result by $3.75. We can find that out by dividing 2.25 by 1, and we get 2.25. Then we do the following....

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Answer:

Step-by-step explanation:

is there more information to the question??

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Answers

Answer:

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Step-by-step explanation:

There are three modes, all numbers have at least two appearances.

Please give thanks by clicking the heart! I solved your other problem too :)

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Step-by-step explanation:

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Answers

Answer:

16

Step-by-step explanation:

To find the greatest number of students that could be in each row, we need to find their greatest common factor. We can list out their prime factors first.

48: 2 × 2 × 2 × 2 × 3

64: 2 × 2 × 2 × 2 × 2 × 2

Here, their common prime factors are 2 × 2 × 2 × 2 which is 16. Thus, the greatest number of students that could be in each row is 16.

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No. of rows in the boys = 64 ÷ 16

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Answer:

Step-by-step explanation:

I believe for this question you need to find the HCF (or GCF you may say) of 48 and 64

HCF - Highest Common Factor

GCF - Greatest common Factor

First, prime factorize 48 and 64 (write them in the product of their prime numbers)

64 = 2 × 2 × 2 × 2 × 2 × 2

48 = 2 × 2 × 2 × 2 × 3

Choose common prime factors (all of them that are common)

on observation, there is 2 × 2 × 2 × 2 common between both of them

which is 16.

So 16 maximum people in each row

Also additional thing, it's fine if some questions were wrong, try and attempt it yourself first before asking it from someone. Getting used to ask someone is going to be troublesome in the long run. If you get stuck, then get help from your teachers (unless the teacher is unco-operative) in which case, seek help from your friends, or talk to your parents about it if you freely share stuff with them.

But anyway, hope that helps ^

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Answers

Answer: 344.7

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  (Cut ^off point at the line)

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344.7000

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Answers

Answer:

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Answer:

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