Positive value b have an absolute maximum at x= 1-b is a local maximum.
g(x) has a point of inflection on the interval 0 < x < infinity for all values of b in the interval (0,2).
To find the absolute maximum of g(x), we need to find the critical points of g(x) and check their values.
g(x) = [tex]xe^(-x) e^(-b)[/tex]
g'(x) = [tex]e^(-x)(1-x-b)[/tex]
Setting g'(x) = 0, we get:
[tex]e^(-x)(1-x-b)[/tex] = 0
This gives two solutions: x = 1-b and x = infinity (since[tex]e^(-x)[/tex] is never zero).
To determine which of these is a maximum, we need to check the sign of g'(x) on either side of each critical point.
When x < 1-b, g'(x) is negative (since [tex]e^(-x)[/tex]and 1-x-b are both positive), which means that g(x) is decreasing.
When x > 1-b, g'(x) is positive (since[tex]e^(-x)[/tex]is positive and 1-x-b is negative), which means that g(x) is increasing.
Therefore, x = 1-b is a local maximum. To determine whether it is an absolute maximum, we need to compare g(1-b) to g(x) for all x.
g(1-b) =[tex](1-b)e^(-1) e^(-b)[/tex]
g(x) = [tex]xe^(-x) e^(-b)[/tex]
Since [tex]e^(-1)[/tex]is a positive constant, we can ignore it and compare [tex](1-b)e^(-[/tex]b) to [tex]xe^(-x)[/tex] for all x.
It can be shown that xe^(-x) is maximized when x = 1, with a maximum value of 1/e. Therefore, to maximize g(x), we need to choose b such that [tex](1-b)e^(-b) = 1/e.[/tex]
(c) To find the points of inflection of g(x), we need to find the second derivative of g(x) and determine when it changes sign.
g(x) = [tex]xe^(-x) e^(-b)[/tex]
g'(x) =[tex]e^(-x)(1-x-b)[/tex]
g''(x) = [tex]e^(-x)(x+b-2)[/tex]
Setting g''(x) = 0, we get x = 2-b.
When x < 2-b, g''(x) is negative (since [tex]e^(-x)[/tex]is positive and x+b-2 is negative), which means that g(x) is concave down.
When x > 2-b, g''(x) is positive (since [tex]e^(-x)[/tex] is positive and x+b-2 is positive), which means that g(x) is concave up.
Therefore, x = 2-b is a point of inflection.
To find all values of b for which g(x) has a point of inflection on the interval 0 < x < infinity, we need to ensure that 0 < 2-b < infinity. This gives us 0 < b < 2.
Therefore, g(x) has a point of inflection on the interval 0 < x < infinity for all values of b in the interval (0,2).
For such more questions on maximum and inflection point
https://brainly.com/question/17328523
#SPJ11
the perimeter if a square is 60 feet, then find the length of the diagonal. if necessary, round to the nearest tenth.
a). 21.2
b). 15
c). 450
d). 30
Answer:
a). 21.2
Step-by-step explanation:
square has 4 sides
one side = 60÷4 = 15
Use pythogoras theorem to find the hypotenuse thus the diagonal of the square.
x = √(15² + 15²)
x = √(225 + 225)
x = √450
x = 21.21 (2 dp)
Help, I'm bad at math XD
1. x = 28
2. x = 13
3. x = 11
4. x = 50
5. x = 53
6. x = 77
7. x = 5
8. x = 70
Which of the following best describes the equation below? y = 5x2 - 7 A. neither linear nor nonlinear B. linear C. both linear and nonlinear D. nonlinear
Answer:
D
Step-by-step explanation:
the answer is
Nonlinear
Tommy buys a football for $20 plus 8% tax John buys a helmet for $25 plus 8% tax what is the difference in the amount Tommy and John paid including tax
Answer:
$5.40
Step-by-step explanation:
First, figure out the cost of the items with tax; for Tommy we have 20*0.08 = 1.6, add that 1.6 to the 20 and his purchase is $21.6, for John we have 25*0.08 = 2, add 2 to his 25 and his purchase is $27. To find the difference we subtract 27-21.6 = 5.4 or $5.40
I need help ASAP pleaseeeeee
Answer: area of smaller is 18 and larger is 45 so the answer is 27
Step-by-step explanation:
What is the difference between -2^4 and (-2)^4
I know the answer but how do you explain it?
Answer:
no difference
When you multiply negative numbers together an even number of times, they change from negative to positive.
Step-by-step explanation:
What is the slope of the line?
y + 2 = -2 ( x - 3 )
A: -1/2
B: -2
C: 1
D: -1
D:) o b what ? you very whell
Step-by-step explanation:
A b. d. c
Answer:
The answer is -2
Step-by-step explanation:
I got this answer on Khan Academy.
Hope this helps! :)
Solve the following equation for p. Select all possible solutions. | p/2-1 |= 0.5
0.5
4
2
3
1
5
Answer:
4
Step-by-step explanation:
The length of a bed would be about
Answer:
2 yards.
Step-by-step explanation:
We know that a length of a bed is DEFINITELY not 2 miles, and it isn't 2 inches either, because they're both too big and too small. However, 2 feet is also pretty small, too, because 2 feet is about the size of a crib. So what's left is 2 yards, so a bed is about 2 yards.
Answer:
2 yards
Step-by-step explanation:
The question is asking what the length of a bed would be.
To answer this question, it's basically common sense, how long is a bed usually, it would be about 5 to 10 feet, big enough to fit a human with no uncomfortability.
So with this info, we can scratch D and B. As for A and C, let's convert them into feet.
1 yard equals 3 feet, meaning two yards would be 6 feet.
1 mile is 5280 feet, this is obviously wrong.
A is our answer.
7) A coat is selling for 3/4 of the original price. The sale price is $180. Write and solve
an equation to determine what the original price of the jacket is.
Answer:
$240
Step-by-step explanation:
Original price: p
discount 25% (multiplier: 0.75)
sale price: $180
p x 0.75 = 180
p = 180/0.75
p = 240
Can you conclude that these triangles are congruent?
Answer:
yes
Step-by-step explanation:
each side is length by with so you can tell these are congruent
Answer:
Yes
Step-by-step explanation:
The reason is because the marks in all of the angles mean the angles are congruent. If the angles match up (1 mark, 2 marks, 3 marks, etc.) then the triangles are congruent.
-2(3x-4)+3x=17 solve for x
x=-3
-6x + 8 + 3x = 17
-3x + 8 = 17
-3x = 17 - 8
-3x=9
x=-9/3
x=-3
please answer as fast as u can
Hey dude, I'm not completely sure but I think the answer's 30°.
In ΔSTU, u = 40 inches, ∠S=73° and ∠T=71°. Find the length of t, to the nearest inch.
Answer: 64 inches
Step-by-step explanation: Solve using sohcahtoa for missing info
Estimate 0.95% of 700
Answer:
6.65
Step-by-step explanation:
0.95% of 700
= 0.0095*700
= 6.65
The value of 0.95% of the number 700 is 6.65.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the number 700 is 0.95%. The number will be calculated as below,
Number = 0.95% of 700
Number = 700 x 0.95/100
Number = 6.65
Therefore, the value of 0.95% of the number 700 is 6.65.
To know more about percentages follow
https://brainly.com/question/24304697
#SPJ6
Running at 5 miles an hour how long will it take you to go 12 miles
Answer:
2 hours and 24 minutes.
Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
5
A. (x + 1)(x - 7)
B. (x + 1)(x + 7)
C. (x - 1)(x - 7)
D. (x - 1)(x + 7)
Answer:
The answer is
(x-1) (x-9)
The factored form of the related polynomial function is [tex](x-1)(x+7).[/tex]
What is polynomial function ?Polynomial function is a function that involves non-negative integer powers or positive integer exponents of a variable in an equation like the quadratic equation, cubic equation.
We have,
In the graph given in question, we can see that [tex]x-[/tex]intercepts the axis twice.
And graphs behave differently at various [tex]x-[/tex]intercepts. Sometimes the graph will cross over the [tex]x-[/tex]axis at an intercept and other times the graph will touch the [tex]x-[/tex]axis and bounce off.
Now, in graph;
The [tex]x-[/tex]intercept at [tex]x=1[/tex], i.e. the solution of the [tex]x-1=0[/tex] and passes through the axis.
Now,
The [tex]x-[/tex]intercept at [tex]x=7[/tex] is the solution of [tex]x-7=0[/tex] and again passes through the axis.
So, from the above statements we can say that the factored form of the related polynomial is [tex](x-1)(x+7).[/tex]
Hence, we can say that the factored form of the related polynomial function is [tex](x-1)(x+7).[/tex]
To know more about polynomial function click here
https://brainly.com/question/14711679
#SPJ2
HELP! 6th grade work due today pleaseeeeee
Answer:
s = 5 feet
Step-by-step explanation:
.................
perfect adjective word chain
Answer:
Tall, light, test, treat.
I think this ans may help you
Jessica and her friends have gone to dinner. When they finished eating their bill came to $82. Jessica decided that she wanted to give a 19% tip
Answer:
97.58
Step-by-step explanation:
Answer: D $15
Step-by-step explanation:
choices
3/4
3/5
5/4
4/5
Answer:
4/5
Step-by-step explanation:
sine is opposite over hypotenuse,
so it's 40/50=4/5
compare by using < > or = between the pairs of numbers l - 8l ____ l2l
here are 15 points if you help me lovely person ;)
Answer:
It is >
Step-by-step explanation:
because the absolute value of -8 is 8 and the absolute value of 2 is 2 so 8 is bigger than 2
Evaluate 3n + 4^2 when n = 2
Answer:
22
Step-by-step explanation:
3n + 4^2
n = 2
3(2) + 4^2 = 6 + 16 = 22
Find the sum:
15.07 +22.8
a. 37.01
b. 37.1
c.37.87
d. 37.78
write an equation in slope intercept form for the line that travels through (1,-2) and (6,8)
Answer:
y=2/1x
Step-by-step explanation:
Subtract (6,8) by (1, -2)
8--2/6-1=10/5
Simply
10/5=2
Plug in
y=2x
What is the value of x?
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
c = x
x^2 = a^2 + b^2
x^2 = 24^2 + 7^2
x^2 = 576 + 49
x^2 = 625
x = 25
need help with this
9514 1404 393
Answer:
f(-2) = 2f(0) = 4Step-by-step explanation:
a) Locate the point -2 on the x-axis. Follow the line up until it meets the blue curve. Follow that grid line to the right to see where it meets the y-axis. It is y=2. That means f(-2) = 2.
__
b) Locate y=4 on the y-axis. Notice that the curve intersects the y-axis there, so x=0.
x = 0 is the only value of x for which f(x) = 4.
Which expression can be used to solve 3/5 ÷ 7/10. A. 5/3×7/10 B. 5/3×10/7 C. 3/5×10/7 D. 3/5×7/10
Answer:
3/5 * 10/7
Step-by-step explanation:
To solve division of fractions
3/5 ÷ 7/10
Use copy dot flip
3/5 * 10/7
Answer:
C) 3/5 x 10/7
Step-by-step explanation:
Can someone help me.
Answer:
A.5,683.0000
B. 1,289,293.0000
C.3,567,920.0000
Step-by-step explanation:
A 15-ft by 15-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 304 ft^2, how wide is the walkway?
Answer:
4 ft = width of walkway
Step-by-step explanation:
It helps if you can draw a figure.
Let x = width of walkway
Length of pool + walkway = (2x + 15)
Width of pool + walkway = (2x + 15)
area of pool and walkway together = (2x + 15)(2x + 15) = [tex]4x^{2} = 60x + 225[/tex]
Area of the pool = 15(15) = 225
Now,
The area of the walkway = area of pool and walkway together - area of pool
304 = 4[tex]x^{2}[/tex] + 60x + 225 - 225
304 = [tex]4x^{2}[/tex] + 60x
4[tex]x^{2}[/tex] + 60x - 304 = 0
4([tex]x^{2}[/tex] +15x - 76) = 0
4(x - 4)(x + 19) = 0
x = 4 x = -19
-19 must be discarded because a length cannot be negative
Therefore x = 4 ft = width of walkway