Consider the following function: f(x) = (x – 5)(x + 1)^2
Enter the x values of any local minima, maxima and inflection points
Answers
Local minimum: x = 5
Local maximum: x = -1
No inflection points.
To find the local minima, maxima, and inflection points of the function f(x) = (x – 5)(x + 1)^2, we need to find its critical points and analyze its concavity.
Step 1: Find the first derivative of f(x):
f'(x) = d/dx [(x – 5)(x + 1)^2]
Using the product rule, f'(x) = (x – 5) * 2(x + 1) + (x + 1)^2
Step 2: Find the critical points by setting f'(x) = 0:
0 = (x – 5) * 2(x + 1) + (x + 1)^2
This equation has two solutions: x = 5 and x = -1.
Step 3: Find the second derivative of f(x):
f''(x) = d^2/dx^2 [(x – 5)(x + 1)^2]
f''(x) = 2(x + 1) + 2(x + 1) + 2(x – 5)
Step 4: Evaluate the second derivative at the critical points to determine their nature:
f''(5) = 2(6) + 2(6) + 2(0) = 24 > 0, indicating a local minimum at x = 5.
f''(-1) = 2(0) + 2(0) + 2(-6) = -12 < 0, indicating a local maximum at x = -1.
There are no inflection points since f''(x) never changes sign.
Your answer:
Local minimum: x = 5
Local maximum: x = -1
No inflection points.
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Related Questions
find the product of (3/-2n) and (4/+2n)
Answers
Answer:
\((\frac{12}{-4n^{2}})\)
Step-by-step explanation:
\((\frac{3}{-2n})(\frac{4}{2n})=(\frac{3*4}{-2n*2n})=(\frac{12}{-4n^{2}})\)
Answer:
\( -\dfrac{3}{n^2} \)
Step-by-step explanation:
\( \dfrac{3}{-2n} \times \dfrac{4}{+2n} = \)
\( = \dfrac{3 \times 4}{-2n \times 2n} \)
\( = \dfrac{12}{-4n^2} \)
\( = -\dfrac{3}{n^2} \)
what is 1/10 as a decimal does it equal 0.1
Answers
Example:
What is 10% of 100?
100 X 0.1 = 10
If 18 people ride in 3 cars how much people ride in 1 car?
Answers
Answer:
6 people per car
Step-by-step explanation:
divide 18 people by 3 cars to get people per cars.
please rate and mark as brainlest.
i hope this help!:)
CAN SOMEONE PLS HELP WITH THIS ASAP!!
Answers
Answer:
What is it?
Step-by-step explanation:
Sung borrowed money from his parents over the last three days. This is represented by the negative values in the table.
What is the total of the values?
What is the average of the values?
Day 1 is negative 4 dollars, day 2 is negative 2 dollars, day 3 is negative 3 dollars.
Answers
Answer:
-$9
-$3
Step-by-step explanation:
So sorry i'm late!
Answer:
I'm terrible at explaining so here's a screenshot
Step-by-step explanation:
Factor Completely
-m^3-2m^2-16m-32
Answers
Answer:
-(m+2)(m^2+16)
Step-by-step explanation:
Solve the following equation: -3 = 1 3/5 + m.
-2 3/5
-4 3/5
-4 2/5
-1 2/5
Answers
Answer:
-4 3/5
Step-by-step explanation:
I subtracted 1 3/5 from -3 and got -4 3/5. I also added 1 3/5 + -4 3/5 to check my work and it is correct.
Free Branliest
Answer please I LONELY PLS GUYS PLEASE
Answers
Answer:
Hello. How's your day been so far?
Step-by-step explanation:
Answer:
Ya
Step-by-step explanation:
Convert 10 centimeters into yards. Round your answer to the nearest hundredth.
Answers
Answer:
0.11 yards
Step-by-step explanation:
To convert centimeters to yards, find the needed unit conversions:
\(cm(\frac{in}{cm})(\frac{ft}{in})(\frac{yd}{ft})\)
Convert centimeters to inches, inches to feet, then feet to yards!
Now replace the values with the correct quantities:
\(10cm(\frac{1in}{2.54cm})(\frac{1 ft}{12 in})(\frac{1 yd}{3 ft})\)
Finally, simplify and cross-cancel the units:
\(0.10936... yd\)
Round to the nearest hundredth:
\(0.11 yd\)
Find the mean of the data set.
{3, 7, 8,4, 1, 1)
A. 3
B. 1
C. 6
D. 4
Please select the best answer from the choices provided
Answers
D. 4
Answer:
D.
Step-by-step explanation:
3+7+8+4+1+1= 24 Once you have that then you divide by all the numbers shown which would be 6. So, 24/6=4
The measure of one interior angle of a parallelogram is 30 degrees more than 2 times mother measure of another angle. Find the measure of each angle
Answers
Answer:
Bsbsjwjajsjajwbwhshwjhehwjwhehwjjqq
Melissa’s family is driving out of state to her grandmother’s house. They know that it takes 20 gallons of gas to get there, and the cost of three gallons of gasoline is $10.50. How much should the family budget to make the one-way trip?
Answers
Answer:
I believe the answer is $70
Step-by-step explanation:
hope I could help
Find the equation of a line that passes through the points (-1,-5) and (-3,-4). Leave your answer in the form y=mx+c
Answers
Answer:
y = -1/2x - 11/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-4 - (-5) / -3 - (-1)
1/ -2
= -1/2
y = -1/2x + b
-5 = -1/2(-1) + b
-5 = 1/2 + b
-11/2 = b
A $350 purchase is discounted 15%. You use a 20% coupon. What is the total paid?
Answers
Answer:
238 should be the answer
Step-by-step explanation:
a jet plane traveling at 480 mph overtakes a propeller plane traveling at 200 mph that had a 3 hour head start. how far from the starting point are the planes?
Answers
The distance of both the planes from the starting point will be 1029 miles.
This is a question of time, speed and distance.
Given that:-
Speed of jet plane = 480 mph
Speed of propeller plane = 200 mph
Also, the propeller plane has a 3 hour head start.
We have to find the distance of both the planes from the starting point.
When the jet plane overtakes the propeller plane both of them would have covered the same distance.
Let the time taken by the jet plane to overtake the propeller plane be t hours.
Hence, the propeller plane would have travelled for (t+3) hours.
Hence, we can write,
480*t = 200*(t+3)
480t = 200t + 600
280t = 600
t = 600/280 = 15/7 hours.
Hence, distance from both the planes from the starting point = (15/7)*480 = 1028.57 miles = 1029 miles.
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What are the coordinates of R', the image of R(-4, 3) after a reflection in the line
y = x
Answers
The coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have:
Image of R(-4, 3) after a reflection in the line y = x
The rule for the reflection over y = x is:
(x, y) = (y, x)
(-4, 3) = (3, -4)
Thus, the coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.
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write the equation of a parabola with focus and directrix
Answers
The equation of a parabola with a given focus and directrix is:
x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0
In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.
To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.
Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).
The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:
sqrt((x - a)^2 + (y - b)^2)
The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.
According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:
sqrt((x - a)^2 + (y - b)^2) = |y - c|
Squaring both sides of the equation eliminates the square root:
(x - a)^2 + (y - b)^2 = (y - c)^2
Expanding and rearranging the terms:
x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2
Simplifying and canceling out the y^2 terms:
x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy
Rearranging the terms to obtain the standard form of the equation:
x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0
Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:
x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0
Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.
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250 pounds = how many tons
Answers
The metric unit from pounds to tons is 250 pounds = 0.125 tons
Converting the metric unit from pounds to tonsFrom the question, we have the following parameters that can be used in our computation:
250 pounds = how many tons
As a general rule, we have
1 pound = 0.0005 tons
Multiply both sides of the equation by 250
So, we have
250 * 1 pound = 0.0005 tons * 250
Evaluate the products
250 pounds = 0.125 tons
Hence, the conversion is 250 pounds = 0.125 tons
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A swimming pool is being constructed so that it is the upper part of aninverted square-based pyramid.a. Calculate H.b. Calculate the volume of the pool.c. How many 6 m3bins will be required to take the dirt away?d. How many litres of water are required to fill this pool?e. How deep is the pool when it is half-filled?
Answers
Answer:
2
Step-by-step explanation:
6 sides by 6 adding 4x4=12
given the function f(x)=4-2x: if the domain is -4,0,5, find the range
Answers
Answer:
The range is 12, 0, -6
Explanation:
Given the function:
f(x) = 4 - 2x
We want to find the range of this function, given that the domain is:
-4, 0, 5
This can be done by replacing x by each element ot the domain in the given function, find f(x).
For element -4
f(-4) = 4 - 2(-4)
= 4 + 8
= 12
For element 0
f(0) = 4 - 2(0)
= 4 - 0
= 0
For element 5
f(5) = 4 - 2(5)
= 4 - 10
= -6
The range is 12, 0, -6
Given the equation \(y=2^x\), predict the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down (2 marks )
Answers
The equation becomes y = 5(2^-(x-2))+5 if the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have equation:
\(\rm y = 2^x\)
Plug x → -x to reflected in the y-axis.
The function becomes:
\(\rm y = 2^-^x\)
For vertical stretch, multiply the function by 5.
The function becomes:
\(\rm y\ =\ 5\left(2^{-x}\right)\)
For translate 2 units, right plug x → (x-2)
\(\rm y\ =\ 5\left(2^{-(x-2)}\right)\)
For translate 5 units, up add 5 to the function.
The function becomes:
\(\rm y\ =\ 5\left(2^{-(x-2)}\right)+5\)
Thus, the equation becomes y = 5(2^-(x-2))+5 if the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.
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![Given the equation [tex]y=2^x[/tex], predict the equation for the graph that has been reflected in the](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/2UDVUbUIjHMuJrDF4GHDKkSNn9TOpy5V.png)
A factory sampled hundreds of 9oz bags of chips off of one of their production lines to make sure the bags had the appropriate
amount of chips. They found the amount of chips to be normally distributed with = 9.12 ounces and o= .05 ounces.
PART A
Given this information, fill out the normal distribution chart below for the weight of 9oz bags of chips from this factory.
Answers
The normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.
What is standard deviation?The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the values deviate from the mean. The most popular way to assess dispersion is standard deviation, which is based on all values.
From the given samples of 9oz of chips we have the following values:
Mean = 9.12 ounces
SD = 0.05 ounces
The normal distribution of the chart below will have the following values:
The mean or the center value of the graph with the highest peak is:
Mean = 9.12
The value to the right of the mean value will be:
Mean + SD = 9.12 + 0.05 = 9.17
Mean + 2(SD) = 9.12 + 2(0.05) = 9.22
Similarly, the value to the left of the mean value will be:
Mean - SD = 9.12 - 0.05 = 9.07
Mean - 2(SD) = 9.12 - 2(SD) = 9.02
Hence, the normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.
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Simplify the expression. -6 1/3-1/2(1/2+x)
Answers
Answer:
-79/12 - x/2
Step-by-step explanation:
Simplify ⏬
Question 1 (1 point)
Stuart Goldman works at King's Golf Spot. He works 11 hours a week and earns $8.25 per hour. What is Goldman's straight-time pay for each
week? (Section 1.1)
a
b
$90.75
$80.75
$80.25
Ος
Od
$90.25
Answers
The amount that Goldman's straight-time pay for each week will be $90.75. Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Stuart Goldman works at Ruler's Golf Spot. He works 11 hours every week and acquires $8.25 each hour.
Goldman's straight-time pay for each week will be given as,
⇒ $8.25 x 11
⇒ $90.75
The amount that Goldman's straight-time pay for each week will be $90.75. Then the correct option is A.
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If Stuart Goldman works at King's Golf Spot. He works 11 hours a week and earns $8.25 per hour. Goldman's straight-time pay for each week is: A. $90.75.
What is straight-time pay?To determine Stuart Goldman's straight-time pay for each week we can multiply his hours worked by his hourly wage:
Straight-time pay = Hours worked × Hourly wage
Let plug in the formula
Straight-time pay = 11 hours × $8.25/hour
Straight-time pay = $90.75
Therefore the correct option is A.
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A company maintains a fleet of vehicles that consist of both cars and trucks. The miles per gallon realized in the cars follows a normal distribution with mean of 30 and a standard deviation of 2 while the miles per gallon realized in the trucks follows a normal distribution with mean of 17 with a standard deviation of 3. Which distribution is more variable?
i. they have the same variability
ii. the mpg for the trucks
iii. the mpg for the cars
iv. there is insufficient information to answer the questions
Answers
Answer:
ii, the mpg for the trucks.
Step-by-step explanation:
A larger standard deviation means more variablilty
Suppose that an individual has a body fat percentage of 12.9% and weighs 169 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.
Answers
Exact: 21.801 rounded to tenth
In a sample of 18 men, the mean height was 178 cm. In a sample of 30 women, the mean height was 152 cm. What was the mean height for both groups put together
Answers
The mean height for both groups put together is 161.75 cm
To find the mean height for both groups put together, we need to calculate the overall mean of all the heights. We can do this by finding the total height of all the men and women and then dividing the total number of people in the sample.
For the men, the mean height was 178 cm. There were 18 men in the sample, so the total height of all the men would be 178 cm x 18 = 3,204 cm.
For the women, the mean height was 152 cm. There were 30 women in the sample, so the total height of all the women would be 152 cm x 30 = 4,560 cm.
To find the total height of all the people in the sample, we can add the total height of the men and the total height of the women: 3,204 cm + 4,560 cm = 7,764 cm.
To find the mean height for both groups put together, we need to divide the total height by the total number of people in the sample. In this case, there were 18 men + 30 women = 48 people in the sample. So, the mean height for both groups put together would be 7,764 cm ÷ 48 = 161.75 cm.
Therefore, the mean height for both groups together is 161.75 cm.
It's important to note that this calculation assumes that the samples are representative of the larger population and that the samples were selected randomly. Additionally, the sample size is relatively small, so the results may not be entirely accurate or representative. However, the calculation gives us a rough estimate of the mean height for both groups put together.
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pls help i don’t understand
Juan claims the solution to the
given system of equations is
unique only to the equations
y = 5x-2 and y = 1/2x +7.
Enter an equation that proves that Juan's
claim is incorrect.
y=_x +_
Answers
An equation such as y = 3x + 5 proves the claim that the solution to the given system of equations is unique to the equations y = 5x-2 and y = 1/2x +7 incorrect.
Solutions of linear equations in two variables are explained as follows in the equations:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
If the a₁ : a₂ = b₁ : b₂ = c₁ : c₂, then the equation has an infinite number of solutions.If the a₁ : a₂ = b₁ : b₂ ≠ c₁ : c₂, then the equation has no solution.If the a₁ : a₂ ≠ b₁ : b₂, then the equation has a unique solution.Thus, to disprove the claim made by Juan we have to form another equation that satisfies the third condition.
And one of those equations can be y = 3x + 5.
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Is y=-1/2x+2 linear? I’m pretty sure it is but just wanna be sure
Answers
Answer:
yes it is
Step-by-step explanation:
yes it is
What is the area of the trapezoid?
Answers
As we know that,
\(\bigstar \: \boxed{\sf {Area_{(Trapezium)} = \dfrac{1}{2} \times ( a + b) \times h}} \\ \)
a and b are length of parallel sides.h denotes height.Substituting values, we get :
\( \longmapsto \) Area = \(\sf \dfrac{1}{2} \) × ( 60 + 40 ) × 30 ft\( \sf ^2 \)
\( \longmapsto \) Area = \(\sf \dfrac{1}{2} \) × 100 × 30 ft\( \sf ^2 \)
\( \longmapsto \) Area = 1 × 100 × 15 ft\( \sf ^2 \)
\( \longmapsto \) Area = 100 × 15 ft\( \sf ^2 \)
\( \longmapsto \) Area = 1500 ft\( \sf ^2 \)
Therefore,
Area of the trapezoid is 1500 ft\( \sf ^2 \)