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
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
Please help me thank you
Answer:
90
Step-by-step explanation:
90
What is Two-thirds divided by StartFraction 4 Over 5 EndFraction?
A fraction bar labeled 1. Under the 1 are 5 boxes labeled one-fifth. Under the 5 boxes are 3 boxes containing one-third. Under the 3 boxes are 15 boxes labeled StartFraction 1 Over 15 EndFraction.
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]
Hence, the required answer is [tex]\dfrac{5}{6}[/tex].
b) Another brand of sheets is on sale 30% off with a regular price of $18.00 per sheet. Which is a better deal, the previous example or this one? Explain. (2 points)
30% OFF EACH SHEET!
30% OFF EACH SHEET!
Answer:
30= 20 so, that’s 10 dollars of
1o+ 7. 5=17. 5+10=27 .50
Step-by-step explanation:
I took the test hope this helps
Jackson painted 80 bird house. 30% of the bird houses were painted green how many green bird houses did Jackson paint
One way to find the total cost of a jacket for $55 with a sales tax of 2%
Answer:
cost of jacket 55
sales tax 2/
55/ 2 percent × 100
2,750
Please help me slove this problem
3x - 3 = 12
Answer:
x=5
Step-by-step explanation:
We kind of have to work backward.
First, we take 12+3 because when we move it over the equal sign, we make it the opposite.
12+3=15
Our new equation is now, 3x=15
We now take:
3x__=15
The blank represents x, which is 5.
Hope this helps!
-AxekickNebulite
What is the equation in slope-intercept form of a line that is perpendicular
to y = 1/3x +2 and passes through the point (3, 1)?
The right rectangular prism below has a square base?Select yes or no.
Answer:
no
Step-by-step explanation:
if it's a prism then it wont have a square bottom
i need help with this one (T_T)
Lin Ying belongs to an athletic club. In 800 m races her times are normally distributed with mean 128 seconds and standard deviation
4 seconds.
(a) What is the probability of her time in an 800 being between 120 and 130 seconds?
(b) What time will she beat in 70% of her races?
Julie belongs to the same club. In 800 m races 85% of her times are less than 140 seconds and 70% are less than 135 seconds. Her times are normally distributed.
(c) Find the mean and standard deviation of Julie's times, each correct to two significant figures.
(d) What is the probability that in an 800 m race Lin Ying will beat Julie?
(e) The club has to choose one of these two athletes to enter a major competition. In order to qualify for the final rounds it is necessary to achieve a time of 114 seconds or less in the heats. Which athlete should be chosen and why?
Answer:
Nine of the times for the first race were at least 16 seconds
Step-by-step explanation:
Here we have from the scatter plot, the times are given as
Time Frequency
19 2
18 2
17 2
16 3
15 1
Therefore, total number of times that are above 16 seconds in the first race is
3 + 2 + 2 + 2 = 9
Therefore, the first option is correct
Answer:
Step-by-step explanation:
The answer is below. Plesetake a look and it will help you
A bag contains 70 coins consisting of quarters and dimes. The total value of coins is $11.50. Which system of equations can be used to determine
the number of quarters, q, and the number of dimes, d, in the bag?
A. d+9= 70
0.100 +0.25q = 11.50
B. d + 9 = 70
0.25d + 0.107 = 11.50
C. d+q = 11.50
0.25d + 0.10g = 70
D. d +9 = 11.50
0.100 +0.25= 70
-4x+3y=-2
y=x-1
x=
y=
Answer:
Easy thankyou for coming to me your answer is x= -1 and y=-2
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
-x-3=-2 simplify by adding 3 to both sides
-x=1
step 6
-x/-1=1/-1 divide
x=-1
second equation
step 1
y=x-1 substitute
y=-1-1
step 2
y=-1-1 simplify
y=-2
answer
x=-1 and y=-2
A string is 5.8 meters long. What is it's length in centimeters
Answer:
a
Step-by-step explanation:
because I said it was jejwjwjeiejehxueh ed uejrhcu
Answer:
580
Step-by-step explanation:
If 100 centimeters are in a meter, then we have to multiply 5.8 by 100 to find out the length of the string in centimeters.
(hope this helped)
Which of the following is equal to 16.4 ?
O A. 32
O B. V16.4
O c.
D. 64
Answer:
b?
Step-by-step explanation:
b= v16.4
PLEASE HELP ME IM TAKING TIMED TEST I WILL MARK YOU AS BRAINLEST!!
Answer:-4.5, -0.5, 0.3, 0.7, 2.3
Step-by-step explanation:
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.
c2+2c
Answer:
Step-by-step explanation:
c2+2c+4
(c+2)^2
^ is the exponent
Each vertical cross-section of the triangular prism shown below is an isosceles triangle.
8
What is the height, h, of the triangular prism?
Round your answer to the nearest tenth.
Answer:
x = 3 unitsStep-by-step explanation:
use Pythagorean theorem:
a² + b² = c²
where a = h
b = 8/2 = 4
c = 5
plugin values into the formula:
h² + 4² = 5²
h² = 5² - 4²
x = √9
x = 3
At ShopRite, chicken sells for $3.75 per pound. How much would it cost to buy 2.25 pounds of chicken?
Answer: 8.4375 U.S. dollars2
Step-by-step explanation:
Answer:
$8.44
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....
2.25 x $3.75 = $8.4375
We got $8.4375 as an answer but we have to remember that when we are talking about money and we have to round to the nearest cent (which is equal to 1 hundredth of a dollar). So now we just have to round to the nearest hundredth, and we get $8.44 as our answer.
A box contains 1 3/4 Pasta how many ounces of pasta are in the box
Answer:
Step-by-step explanation:
is there more information to the question??
The following list gives the number of siblings for each of 8 students. 3, 4, 2, 1, 2, 0, 3, 0 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."
Answer:
3, 2, 0
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 :)
A car travels 180 miles in 3 hours. how far did it travel in 1 hour
Answer:
60
Step-by-step explanation:
pls helpppppppppppp
Marita always listen to her favourite radio station when she drives her car
Everymoarning she listen to her radio
Please only correct answer
Answer:
second vala hai correct Answer
Answer:
[tex](\sqrt{x})^{2} = \sqrt{x^{2} }[/tex]
guys help I am stuck on this question I have to send my winter holiday
48 girls and 64 boys belong to the Twelve Mile Coulee School choir. The choir teacher plans to arrange the students into equal rows (the same number of students in each row). Only girls or boys will be in each row. What is the greatest number of students that could be in each row?
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.
No. of rows in the girls = 48 ÷ 16
= 3
No. of rows in the boys = 64 ÷ 16
= 4
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 ^
what is 344.7234 to 1 decimal point
Answer: 344.7
Explanation:
344.7∣234
(Cut ^off point at the line)
The digit to the right of the cut of the point is less than 5. So the digit to its left (the 7) is not changed and all those to the right are changed to 0 gives you:
344.7000
Written as 344.7
Hope this helps and hope you have a wonderful day :)
find the multiplicative inverse of -2 in mod 7
Answer:
So something mod 7 is -2Lets consider what mod does as a commands: If you have 7 and then mod it by 2 ie 7%2 you get 1 Essentially mod is seeing how many times a # goes into the other number and finding the remainder. In this case we want the remainder of 2: -8%3 =-2note there is also a mathematical procedural way to solve this.Rate positively and give brainlistWhich of the following most likely causes the rate of a chemical reaction to increase? (5 points)
a
Decreasing the reaction temperature
b
Slowing down the reacting molecules
c
Taking away heat from the reaction
d
Adding heat to the reaction
Answer:
i think adding heat to reaction will change the rate of the reaction
wirte the fractional coefficient for 1 1/4
00:00
What is the number of terms in this expression?
m
5
+4x6
5
Enter your answer in the box.
Answer:
40
Step-by-step explanation: