Consider the function g(x) = (x-e)^3e^-(x-e). Find all critical points and points of inflection (x, g(x)) of the function g.

Answers

Answer 1

Answer:

The answer is "[tex]cirtical\ points \ (x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})[/tex]"

Step-by-step explanation:

Given:

[tex]g(x) = (x-e)^3e^{-(x-e)}[/tex]

Find critical points:

[tex]g(x) = (x-e)^3e^{(e-x)}[/tex]

differentiate the value with respect of x:

[tex]\to g'(x)= (x-e)^3 \frac{d}{dx}e^{e-r} +e^{e-r} \frac{d}{dx}(x-e)^3=(x-e)^2 e^{(e-x)} [-x+e+3][/tex]

critical points [tex]g'(x)=0[/tex]

[tex]\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3[/tex]

So,

The critical points of [tex](x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})[/tex]


Related Questions

What is ideal or real solution?

Answers

Answer:

An Ideal solution follows the Raoult's law strictly

A Real solution shows deviation from the Raoult's law.

Step-by-step explanation:

Mav is making pizzas for a pizza party. Each pizza requires 4/5 pound of cheese. How many pounds of cheese does she need to make 5 pizzas? Express your answer in simplest form.

Answers

Answer:

4 pounds of cheese

Step-by-step explanation:

4/5*5=4

what is the estimate value of

Answers

Answer:

1.99

Step-by-step explanation:

Pi is 3.14

So result is 1.99

Need help ASAP! Due very soon please help

Answers

Answer:

Lemme get you numba first

Answer:

y = -3/4x + 36

Step-by-step explanation:

You move down three spaces and over 4 spaces on the graph

36 is the y intercept of the line

Find the Highest Common Factor (HCF) of 36 and 48

Answers

Answer: 12

Step-by-step explanation:

The answer of this question is 12

Cual es mayor 0.08 o 0.2

Answers

Answer:

0.2

Step-by-step explanation:

Answer:

0.2 es mayor.

Step-by-step explanation:

0.2>0.08

Find and state the inverse of the function, and also state whether the inverse is a function.
((3,5), (2,8), (1.5), (0.3))

Answers

The inverse of the function is {(5, 3), (8, 2), (5, 1), (3, 0)} and it is not a function

How to determine the inverse of the function

From the question, we have the following parameters that can be used in our computation:

((3,5), (2,8), (1.5), (0.3))

The above ordered pairs can be represented a

(x, y)

This means that the inverse function is

(y, x)

So, we have the following expression

(y, x) = {(5, 3), (8, 2), (5, 1), (3, 0)}

Also, the inverse is not a function

This is so because the x value 5 has different y values 3 and 1

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The mode of the raw data given as: 4, 7, 4, 3, 2, 7, 7, 6, 4, 7, 8

Answers

Answer:

7, since it is the number that pops up the most in the set of data given here

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

The sum of two consecutive even numbers is 34. What numbers is it

Answers

Answer:

16 and 18

16 + 18 = 34 .......... .....

The cost of Katie’s meal at a restaurant is $15.00. She is charged 7.0% tax and leaves a tip of x dollars. Katie spent a total of $20.05 on the meal, tax, and tip.

Answers

Answer:

$5.05

Step-by-step explanation:

The circumference is 79.5
Need help with finding the diameter and radius

Answers

Answer:

Step-by-step explanation:

[tex]C=\pi D[/tex]

[tex]79.5=\pi D\\[/tex]

divide by [tex]\pi[/tex]

D = 25.30

radius = [tex]\frac{d}{2}[/tex]

[tex]\frac{25.30}{2} =12.65[/tex]

Answer:

r approx 12.7

d approx 25

Step-by-step explanation:

How do you graph 3 4 on a number line?

Answers

By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 8 equal parts we can graph 3/4 on the number line, where 3/4 = 6/8, which will be equal to the sixth part from the left end.

A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

For drawing 3/4 on a number line, we will follow the following steps:

We will first draw a line and mark 0 and 1 on it.

In between 0 and 1, we will divide the total distance into 8 equal parts, where one part will represent (1/8)th portion.

As 3/4 can be written as 6/8 which will be equal to 6 parts out of those 8 parts.

Hence. by marking there we can locate 3/4 on the number line.

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The correct question should be like:
How do you plot 3/4 on number line

8/9 to what power equals 64/81

Answers

2nd

Step-by-step explanation:

8/9 to the second power equals to 64/81. Hope this helps!

Answer:

Hi  

x = exponent  

64 = 8·8 = 8^2

81 = 9·9 = 9^2

64/81 = 8^2/9^2 = (8/9)^2

(8/9)^2 = (8/9)^x

 

x = 2

Step-by-step explanation:

Please consider giving me brainliest.

210 students were asked whether they want to go to a water park or a roller skating rink for a class party.
I
• 50 students are girls who want to go to the water park.
• 45 students are girls who want to go skating.
60 students are boys who want to go to the water park.
Water park Skating Total
Boys
60
55
115
Girls
50
45
95
Total
110
100
210

Answers

Answer:

60.3

Step-by-step explanation:

hope this helps

Find the midpoint between these points.
(1,3) (5.1)
someone please help asap !!!

Answers

Answer:SOLUTION

The midpoint for two points P=(px,py) and Q=(qx,qy) is M=(px+qx2,py+qy2).

We have that px=1, py=3, qx=5, qy=1.

Thus, M=(1+52,3+12)=(3,2).

ANSWER

M=(3,2)A

Step-by-step explanation:

Answer:

The midpoint is (3, 2)

Step-by-step explanation:

To find the x-coordinate of the midpoint, average the x-coordinates 1 and 5:

          1 + 5

xm = ----------- = 3

              2

y-coordinate:

          1 + 3

ym = ----------- = 2

              2

The midpoint is (3, 2)

5
Isabella wants to create 23 ounces of new hand lotion, with a minimum 15% concentration of beeswax, from a mixture of two lotions.
One lotion has a 21% concentration of beeswax, and the second lotion has a concentration of 5% beeswax. Based on the inequality
below, how much of the 21% lotion, x, will she need?
O A. x≥ 14.375
O B.
x2 15.33
OC.
x2 20.125
O D. x2 11.5
0.21x+0.05(23-x) ≥ 3.45

Answers

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

What are Inequalities?

The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

In order to get the variable on its own, you can solve a lot of straightforward inequalities by adding, removing, multiplying, or dividing the two sides. But as a result of them, the direction of the inequality will change: Using a negative number to divide or multiply both sides. right and left sides are switched.

An inequality results from the comparison of two or more algebraic expressions using the symbols, >, or. They are the mathematical expressions with unequal sides.

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Find value of y

[tex] {y}^{2} - 58 = 25 \times 4 + 11[/tex]

Answers

Hello there!

Answer:

y = ± 13

Step-by-step explanation:

[tex]y {}^{2} - 58 = 25 \times 4 + 11 \\ y {}^{2} - 58 = 100 + 11 \\ y {}^{2} - 58 = 111 \\ y {}^{2} - 58 - 111 = 111 - 111 \\ y {}^{2} - 169 = 0 \\ (y + 13)(y - 13) = 0 \\ y = - 13 \: \: \: and \: \: \: y = 13[/tex]

Please answer all with explanation

Answers

Answer:

1:Exponents are not involved..try this 34% 1/2 + ==% 98) ::*37 21 /) ( ^ 11 56/77

2:make a little close parenthesis and make a little = and % x2 RX then multiply it 9 by 9

3:477/^54*(7632)**% 87÷32×(76*09×23) 2/8=97

4:9a/(92 28 ^^_× (32

Step-by-step explanation:

HOPE IT HELPS!!

How do you convert log to the base e to log to the base 10?

Answers

To convert the log base 2 to log base 10, we can use the change of base formula for logarithms. The change of base formula for logarithms is as written:

log b(x)=logc(x) logc(b)

By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:

log2(x)=log10(x)log10(2)=log(x)log(2)

This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.

The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is denoted as “log e e”.

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What is the revolution of the Earth and Moon?

Answers

The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes time of 365.24 days, and the Moon's revolution takes 27.32 days.

The revolution of the Earth and Moon is the path of the two celestial bodies around the Sun. The Earth takes 365.24 days to complete one revolution, which is also known as one year. The Moon, on the other hand, takes 27.32 days to complete one revolution, which is also known as one lunar month.

The revolution of the Earth and Moon refers to their orbits around the Sun, with the Earth taking 365.24 days and the Moon taking 27.32 days to complete one revolution.The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes 365.24 days, and the Moon's revolution takes time of  27.32 days.

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-16x-32y=52 solve for y

Answers

Answer:  I think 7/2?

Step-by-step explanation:

solve (x-3)^2=49. select the values of x

Answers

Answer:

x1=-4 x2=10

Step-by-step explanation:

step 1: x-3 = +/- 7 <--- take the square roots of both sides of the equation and use both positive and negative roots

step 2: x-3 = -7

            x-3=7

step 3: x-3=-7--> x=-4

           x-3=7--> x=10

step 4:x1=-4, x2=10 is the answer

Ron killed 8 times as many spiders as Harry,H (Write an expression to represent the following situations)

Answers

Answer:

Ron killed 8 times as many spiders as Harry: R = 8 * H

Step-by-step explanation:

This expression represents the situation in which Ron killed 8 times as many spiders as Harry.

If you buy 3 CD’s at the original cost of 9.99 but you have a 10% off coupon and the sales tax is 6% what is your total

Answers

9.99-10%=8.99
+6%=$9.53

hello i need urgent help with this assignment.

Answers

Answer:

AD = 1 3/4y + 5/8x - 3

Step-by-step explanation:

AD = 1/4x + 2y + 3 - 1/4y + 3/8x - 6

combine like terms:

AD = 1 3/4y + 5/8x - 3

5. The base of a rectangular prism has
an area of 23 square cm. The height of
the rectangular prism is 3 cm. What is
the volume of this rectangular prism?

Answers

Answer:

1. length×width × height

4×9×10

=360cm

2.base×height

36×65

=2340 inches

Find the volume and round to the nearest hundredths place when necessary.

Answers

Answer:

This is a prism since both sides are the same triangle,

Lets find the area of the triangle first then multiply it by the width which is 16.

20.5(base or height) x 13.3(height or base) = 272.65

272.65 divided by 2 ( x 1/2) = 136.325 is your area, now we multiply by the width.

136.325 x 16 = 2,181.2 mm3 is your volume.

Whenever coming across these types of volumes we must first find a shape and find its area then multiply it by the figure's height.

Formula area of a triangle:

B(base) x H(height) x 1/2(basically just dividing by 2)

What are 3 examples of perfect squares?

Answers

Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.

What is perfect squares?

Perfect squares are numbers that can be expressed as the product of two equal integers, such as 4, 9, and 16. These numbers can be written as the square of a single number, such as 2² = 4, 3² = 9, and 4² = 16. Perfect squares are also known as whole squares, and they provide an easy way to find the square root of a number.

Perfect squares are numbers that are the result of multiplying a number by itself. For instance, 4 is a perfect square because it is equal to 2 x 2.

Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.

For example, the square root of 16 is 4, since 4 x 4 = 16.

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Which of the following points is a solution to the system of equations shown?

y - x = -1

x + y = -5

Answers

`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.

[tex]\quad \qquad \huge \bf \dag \: Answer \: \dag[/tex]

`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.

[tex] \underline{ \large \rm Solution} : [/tex]

[tex]\rm Given : [/tex]

Two equations are -

y - x = -1 (i)

x + y = -5 (ii)

[tex] \rm Procedure : [/tex]

Considering the equations as (i) and (ii) respectively

From equation (i) -

y = x - 1

put this value of y in equation (ii) -

x + y = -5

x + x - 1 = -5

2x = -5 + 1

2x = -4

x = -2

Next thing to do would be to put value of x we got in equation (i) to get y

y - x = -1

y - (-2) = -1

y + 3 = -1

y = -1 - 3

y = -4

Values asked are :

[tex] \rightarrow \rm y = - 4[/tex]

[tex] \rightarrow \rm x= - 2[/tex]

`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.

[tex] \large \bf hope \: \: it \: \: helps \: - dabI [/tex]

`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.

What is the Average Rate of Change of the graph below from -5 < t < 8

Answers

Answer:47

Step-by-step explanation

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