Answers
Answer:
[tex]\frac{dy}{dx} =\frac{-8}{x^2} +2[/tex]
[tex]\frac{d^2y}{dx^2} =\frac{16}{x^3}[/tex]
Stationary Points: See below.
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesCalculus
Derivative Notation dy/dx
Derivative of a Constant equals 0.
Stationary Points are where the derivative is equal to 0.
1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undefBasic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]f(x)=\frac{8}{x} +2x[/tex]
Step 2: Find 1st Derivative (dy/dx)
Quotient Rule [Basic Power]: [tex]f'(x)=\frac{0(x)-1(8)}{x^2} +2x[/tex]Simplify: [tex]f'(x)=\frac{-8}{x^2} +2x[/tex]Basic Power Rule: [tex]f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}[/tex]Simplify: [tex]f'(x)=\frac{-8}{x^2} +2[/tex]Step 3: 1st Derivative Test
Set 1st Derivative equal to 0: [tex]0=\frac{-8}{x^2} +2[/tex]Subtract 2 on both sides: [tex]-2=\frac{-8}{x^2}[/tex]Multiply x² on both sides: [tex]-2x^2=-8[/tex]Divide -2 on both sides: [tex]x^2=4[/tex]Square root both sides: [tex]x= \pm 2[/tex]Our Critical Points (stationary points for rel max/min) are -2 and 2.
Step 4: Find 2nd Derivative (d²y/dx²)
Define: [tex]f'(x)=\frac{-8}{x^2} +2[/tex]Quotient Rule [Basic Power]: [tex]f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2[/tex]Simplify: [tex]f''(x)=\frac{16}{x^3} +2[/tex]Basic Power Rule: [tex]f''(x)=\frac{16}{x^3}[/tex]Step 5: 2nd Derivative Test
Set 2nd Derivative equal to 0: [tex]0=\frac{16}{x^3}[/tex]Solve for x: [tex]x = 0[/tex]Our Possible Point of Inflection (stationary points for concavity) is 0.
Step 6: Find coordinates
Plug in the C.N and P.P.I into f(x) to find coordinate points.
x = -2
Substitute: [tex]f(-2)=\frac{8}{-2} +2(-2)[/tex]Divide/Multiply: [tex]f(-2)=-4-4[/tex]Subtract: [tex]f(-2)=-8[/tex]x = 2
Substitute: [tex]f(2)=\frac{8}{2} +2(2)[/tex]Divide/Multiply: [tex]f(2)=4 +4[/tex]Add: [tex]f(2)=8[/tex]x = 0
Substitute: [tex]f(0)=\frac{8}{0} +2(0)[/tex]Evaluate: [tex]f(0)=\text{unde} \text{fined}[/tex]Step 7: Identify Behavior
See Attachment.
Point (-2, -8) is a relative max because f'(x) changes signs from + to -.
Point (2, 8) is a relative min because f'(x) changes signs from - to +.
When x = 0, there is a concavity change because f"(x) changes signs from - to +.
Related Questions
The figure is made from squares of different sizes.Find the area of A if the side of each of the two indentical smallest square is 2cm.
Answers
segmant ce and segment fh are parellel lines
Answers
Answer:
is this really a question. I don't understand it you need an explanation of what you're asking us.
Step-by-step explanation:
-4 (-3 + 5 + (-2)) show all steps
Answers
Answer:
0
Step-by-step explanation:
-4(-3 + 5 + (-2))
-4(-3 + 5 -2)
-4 • 0
0
Answer:
= 0
Step-by-step explanation:
-4(-3 + 5 +(-2 ))
get rid of the "( )"
-4 (- 3 + 5 - 2)
calculate the sum
-4 x 0
anything times 0 = 0 so the answer is;
0
Write a recursive formula for the arithmetic sequence:
7,4,1,-2
Answers
a(sub)n = a(sub)n-1 - 3
(sub) indicates the values touching the parenthesis are written as a subscript.
The above would be the recursive formula as you are taking the previous number and subtracting 3 to get the next number in the sequence.
Answer:
N - 3
Step-by-step explanation:
It is a series of -3 so:
7 -3 = 4
4 - 3 = 1
1 - 3 = -2
So:
N-3
where N is the present value in the sequence.
2. What is the value of 9x – 4y if x = 3 and y = 2?
F. 12.
G. 19
H. 93
1. 27
H
Answers
Answer:
G. 19 is your answer dear
Step-by-step explanation:
9(3)-4(2)
27-8 = 19
Choose the value to make the equation true.
70
.
9
÷
Choose...
=
7
.
09
Answers
Step-by-step explanation:
= 7 . 09
I am having a hard time with simultaneous equations specifically the elimination method, i want to know when do we subtract and when do we add, so if u know how its done plz help im confused
Example :
3x-2y =7
4x+y = 13
Plz solve it too-
Answers
Answer:
The solution to these two equations is (3, 1)
Step-by-step explanation:
So for the elimination method, we are basically multiply each equation by a factor that would allow us to cancel them out..
We could rewrite the equations as the following to make the elimination method easier:
-2y + 3x = 7
y + 4x = 13
We could multiply the second equation by positive 2 in order to cancel out the y from the first equation when we add.
-2y + 3x = 7
2y + 8x = 26 ---> Now we have 11x = 33, when we simplify, we have x = 3.
Now to find our y value in order to find the solution, we would just plug in our x value and solve for y. **We can use either equation to find the answer for this...
-2y + 3x =7.
-2y + 3(3) = 7
-2y + 9 = 7
-2y = -2
y = 1.
We can double check our answer by plugging in both x and y values into the second equation.
4(3) + 1 = 13.
12 + 1 = 13, so we are correct.
The solution to these two equations is (3, 1)
Sebuah LSM akan mengirim 5 utusan untuk mengikuti suatu konferensi. Kelima utusan tersebut terdiri dari 3 wanita dan 2 pria. Kelima orang tersebut akan dipilih dari pengurus harian yang terdiri dari 6 wanita dan 3 pria. Peluang memilih ke lima utusan tersebut adalah
Answers
Billy jarred 3.87 liters of jam after 3 days. How many days does Billy need to jar 15.48 liters of jam in all?
Answers
Answer: 12 days
Step-by-step explanation:
3.87/3=1.29 liters of jam in 1 day
1.29*12=15.48 liters in 12 days
Answer:
12 days
Step-by-step explanation:
Pls i need help with my math
Find the value of each symbol in the multiplication table below:
Answers
Answer:
Step-by-step explanation:
Chili = 3
lime = 1
salt = 9
avocado = 6
guacamole = 18
Y=4x+2
A) Identify the slope (4,-2)
B)Identify the y-intercept:-2
Answers
Answer:
4 - slope
2 - y - intercept
Step-by-step explanation:
The equation is in slope-intercept form.
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The '4' is the slope of the equation.
[tex]y=\boxed{m}x+b\\\\y=\boxed{4}x+2[/tex]
The '2' is the y-intercept.
[tex]y=mx+\boxed{b}\\\\y=4x+\boxed{2}[/tex]
Hope this helps.
Mary sees 40 elephants and 15 baby elephants at the zoo. What is the ratio of elephants to baby elephants?
Answers
Answer:
8:3
Step-by-step explanation:
You divide them both by 5.
Answer:
40:15 = 8:3
Step-by-step explanation:
This is the answer because:
1) Since there are 40 elephants and 15 baby elephants, the answer would be 40:15, but we want to simplify the ratio. In order to simplify the ratio, just divide each number by 5:
40 ÷ 5 = 8
15 ÷ 5 = 3
8:3
Therefore, the answer is 8:3.
Hope this helps! :D
PLZZZZZZZZZZZZZZZZZZZZZZZZ HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Simplify the following expressions using the properties of exponents.
Use "^" to indicate exponents. For example, x^5 to represent x^5.
a.
(2^−4)^−4 divided by 24 x 22
b. This problem has been started for you. Finish simplifying the problem.
2a^−1×(4a^2)^−2 divided by 4a^0
=
2a^−1×4^−2 a^−4 divided by 4a ^0
=
2 divided by 4a^0xa^1x4^2 a^4
PLZZZZZZZZZZZZZZZZZZ SHOW WORK
Answers
Answer:
A. = 60074.6 (The 6 is repeating forever)
Step-by-step explanation:
May I have brainliest please? :)
Find the product of and 4/5 and 5/10
Answers
Answer:
1/3
Step-by-step explanation:
4 • 1/12
1/3
Answer:
2/5
Step-by-step explanation:
The sum of five times a number and seven is 107. Find the number.
Answers
5x = 100
X = 20
The number is 20
Answer:
20.
Step-by-step explanation:
Let the number be x.
5x + 7 = 107
5x = 107 - 7
x = 100 / 5
x = 20
Hope this helped!
need help on 5 & 6 please !!!
Answers
Step-by-step explanation:
Q5. Let the cost of 28subscriptions be $s.
Words: 1subscription/28subscription = $21/$28
Numbers: 1/28 = 21/s
Cross multiply and solve: 1 x s = 21 x 28
s = 588
Answer with label: $588
Q6.
Words: 2inches/3.6inches = 2.5hours/bhours
Numbers: 2/3.6 = 2.5/b
Cross multiply and solve:
2 x b = 2.5 x 3.6
2b = 9
b = 4.5
Answer with label: 4.5hours
Write a quadratic function whose graph has the given characteristics.
vertex: (3, 5)
point: (2, –1)
Answers
Y = a( x - 3)^2 + 5
Solve for a
-1 = a( 2 - 3) ^ 2 + 5
-1 = a (-1)^2 + 5
-1 = a + 5, a = -6
Equation: y = -6 (x - 3) ^2 + 5
How do I solve this equation and find the solutions?
Answers
Answer:
x = 10
Step-by-step explanation:
x-sqrt(2x+5) = 5
2x+5 = 25-10x+x^2
x = 10
Hope this helped!
Answer:
x = 5
Step-by-step explanation:
x - 5 = [tex]\sqrt{2x+5}[/tex] ( x > 5)
(x - 5)² = ( [tex]\sqrt{2x+5}[/tex] )²
x² - 10x + 25 = 2x + 5
x² - 12x + 20 = 0
(x - 10)(x - 2) = 0
[tex]x_{1}[/tex] = 10
[tex]x_{2}[/tex] = 2 strange root, does not satisfy the condition x > 5 ( 2 - [tex]\sqrt{2*2+5}[/tex] ≠ 5 )
10 - [tex]\sqrt{2*10+5}[/tex] = 5
10 - 5 = 5
5 = 5
(256x^256)^3/8 please answer to this question
Answers
Answer:
The answer is 8x^96.
Hope this helps and if you could mark me as brainliest. Thanks!
8x⁹⁶ is the simplified form of the expression.
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here, the expression as (256x²⁵⁶)^³/₈
=(256)^³/₈ × (x²⁵⁶)^³/₈
=(2⁸)^³/₈ × (x³²)^³
=2³ × x⁹⁶
Hence, the answer is 8x⁹⁶
Learn more about Polynomials here:
https://brainly.com/question/11536910
#SPJ2
help i need it badly
Answers
Answer:
x^2+3x-10 that should be your answer
Answer:
x^2+3x-10
Step-by-step explanation:
you have to expand the polynomial using the foil method.
Simplify
(35)2
3-2
312
39
38
310
Answers
Answer: The answer is 3^12.
Step-by-step explanation:
Answer:
3^12
Step-by-step explanation:
I need help asap please
Answers
Answer:
-3 or decreasing by 3
Step-by-step explanation:
To find the average change, you only care about the first and last point which would be (3,17) and (8,2)
the overall change during that time is 2-17=-15 (for the f(x) side )
the overall change during that time is 8-3=5(for the x side)
all we have to do is -15/5=-3
therefore the average rate of change is -3
Why is the solution of 3x + 5 = 2x - 7
Answers
Answer:
Use pemdas
Step-by-step explanation:
Paranthese, e, multiplacation, division, addition, subtraction
Answer:
Its option A
where the lines intersect x satisfies both y = 3x+5 and y = 2x - 7
Step-by-step explanation:
1300 people attended a baseball game. 936 of the people attending supported the home team, while 364 supported the visiting team. What percentage of people attending supported the home team?
Answers
Answer:
72
------------------------------------------
100⋅936=
\,\,\color{orange}{1300}\cdot\color{blue}{x}
1300⋅x
Cross multiply
\frac{93600}{1300}=
1300
93600
=
\,\,\frac{1300x}{1300}
1300
1300x
Divide both sides by 25
\color{blue}{72\%}=
72%=
x
Simplify
There are 32 radios , 8 of them are out of order. what percent of radios are out of order ?
chapter in maths is comparing quantities need answer fast pls.
Answers
Answer:
[tex]\large\boxed{\fcolorbox{blue}[/tex]
Answer:
25%
Step-by-step explanation:
8÷32
= 0.25 x 100
= 25%
find the value of 5/22×(3/7×(-6/11))and (5/22×3/7)×(-6/7) compare them what do you observe
Answers
this is the solution.the diff is the order of the number and the number.
Answer:
After comparing we observe both equations have different answers.
Step-by-step explanation:
Find the value of [tex]\frac{5}{22}\times (\frac{3}{7}\times (-\frac{6}{11}))[/tex] and [tex](\frac{5}{22}\times \frac{3}{7})\times (-\frac{6}{7})[/tex]
Solving [tex]\frac{5}{22}\times (\frac{3}{7}\times (-\frac{6}{11}))[/tex]
[tex]=\frac{5}{22}\times (\frac{3}{7}\times -\frac{6}{11})\\=\frac{5}{22}\times (-\frac{18}{77})\\=\frac{5}{22}\times -\frac{18}{77}\\=\frac{5}{11}\times -\frac{9}{77}\\=-\frac{45}{847}[/tex]
Now solving [tex](\frac{5}{22}\times \frac{3}{7})\times (-\frac{6}{7})[/tex]
[tex]=(\frac{15}{154})\times (-\frac{6}{7})\\=\frac{15}{154}\times -\frac{6}{7}\\=\frac{15}{77}\times -\frac{3}{7}\\=-\frac{45}{539}[/tex]
After comparing we observe both equations have different answers.
Find the product. Estimate to check if the answer is reasonable.
195x4
Answers
Answer:
780
Step-by-step explanation:
Estimate: 200 x 4 = 800
Answer:
780
Step-by-step explanation:
The product of 195×4
=780.
The answer is 780.
Given the figure below, find the measure of
Answers
Answer:
24°
Step-by-step explanation:
m∠DCE = 180° - 90° - 41° - 25° = 24° (angles on a straight line are supplementary)
This is a question on angles . If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Plz help!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
c = 5n
Step-by-step explanation:
The cost is equal to the price times the number of notebooks
verify experin mentally that the vertically
opposite angles are equally.