Find the intervals on which f is increasing and decreasing, find the local maximum and minimum values of f, find the intervals of cocavity and inflection f(x) 2x^3 + 3x^2 -36x
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Increasing: x ∈ (-∞, -3) ∪ (2, ∞)
Decreasing: x ∈ (-3, 2)
Local maximum: (-3, 81)
Local minimum: (2, -44)
Concave downward: x ∈ (-∞, -0.5)
Concave upward: x ∈ (-0.5, ∞)
Point of inflection: (-0.5, 18.5)
Related Questions
If f(3) = 11 and f '(x) ≥ 2 for 3 ≤ x ≤ 8, how small can f(8) possibly be?
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f'(x) can only be 2 and not less so then f(x) would increase by 2 for every x increasing by 1 all the way to x=8.
So then smallest possible f(8) would be f(8) = f(3) + 2 + 2 + 2 + 2 + 2 = f(3) + 2(8-3) = 21
Hope this helps.
Given the derivative f '(x) ≥ 2, the function f(x) increases by at least 2 units for every increase in 'x' from 3 to 8. Therefore, the smallest possible value of f(8) is reached when the increase is exactly 2 per 'x', giving us a result of 21.
Explanation:
The question is about calculus, specifically related to the concept of derivatives and their role in function interval analysis. Given the information that f(3) = 11 and f '(x) ≥ 2 for 3 ≤ x ≤ 8, we are asked to find the smallest possible value of f(8).
The derivative, f '(x), represents the rate of change of the function f(x). It is mentioned that f '(x) ≥ 2, which means that the function f(x) is increasing at a rate not less than 2 units per increase in 'x' from 3 to 8.
This suggests that the smallest possible value of f(8) could be achieved by assuming that f(x) increases exactly by 2 units for every increase in 'x'. So, from x = 3 to x = 8 is a change of 5 units in 'x'. Multiply this by the rate of change 2 to obtain the total change in f(x), which is 5 * 2 = 10. Added to the initial value f(3) = 11, we get the smallest possible value for f(8) is 11 + 10 = 21.
Learn more about Derivatives here:https://brainly.com/question/32963989
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Fill in the blank 300mm =___m
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Final answer:
To convert 300mm to meters, divide 300 by 1000 because there are 1000 mm in a meter, resulting in 0.3 meters.
Explanation:
To convert millimeters to meters, we use the conversion factor that 1000 mm equals 1 m. Therefore, to convert 300mm to meters, you divide 300 mm by 1000 because there are 1000 mm in a single meter. So, let's carry out the calculation:
300 mm ÷ 1000 = 0.3 m
Thus, 300 mm is equal to 0.3 meters.
helppppppppppppp stat
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A right cylinder has a radius r of 19.4 cm and a height h of 48.3 cm. what is the volume of the cylinder in m3
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which quadratic equation equation is equivalent to (x^2-1)^2 -11(^2-1) +24=0
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Use substitution: [tex]x^2-1=t[/tex]
[tex]t^2-11t+24=0\\\\t^2-8t-3t+24=0\\\\t(t-8)-3(t-8)=0\\\\(t-8)(t-3)=0\iff t-8=0\ \vee\ t-3=0\\\\t=8\ \vee\ t=3[/tex]
we're going back to substitution:
[tex]x^2-1=8\ \vee\ x^2-1=3\ \ \ \ |add\ 1\ to\ both\ sides\ of\ the\ equations\\\\x^2=9\ \vee\ x^2=4[/tex]
therefore
[tex]x=\pm\sqrt9\ \vee\ x=\pm\sqrt4\\\\\boxed{x=-3\ \vee\ x=3\ \vee\ x=-2\ \vee\ x=2}[/tex]
Answer:
x = ± 3 and ± 2
Step-by-step explanation:
The given quadratic equation is
[tex](x^{2}-1)^{2}-11(x^{2}-1)+24=0[/tex]
To make this question easier we will consume ( x² -1 ) = a
a² - 11a + 24 = 0
Now we can factorize this equation easily
a²- 8a - 3a + 24 = 0
a (a-8) - 3 ( a-8) = 0
( a-3 ) ( a-8 ) = 0
Therefore, a - 3 = 0 ⇒ a = 3
or a - 8 = 0 ⇒ a = 8
Now we put the value a
when a = 3 (x² - 1) = 3
x² = 3 + 1 = 4
x = √4
= ± 2
when a = 8 (x² - 1) = 8
x² = 9
x = √9
= ± 3
Therefore, x = ± 3 and ± 2 will be the answer.
The poplution of Las vegas, Nevada has been increasing at an annual rate of 7.0%. If the poplution of las vegas was 478,434 in the year 1999, predict its population in 2010.
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p(x) = 478,434*1.07^x
For x=11, this is
p(11) = 478,434*1.07^11 ≈ 1,007,033
The relation predicts the Las Vegas population in 2010 to be 1,007,033.
The base of an isosceles triangle is 7 cm longer than the legs. Find the legs if the perimeter of the triangle is 43 cm.
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43 cm = L + L + (L +7 cm)
36 cm = 3L
12 cm = L
The length of the legs is 12 cm.
solve for x z= 19+2 (x+y)
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Hope it helps
(Giving Brainliest)
what is the solution to...
[tex]|x| +19 \leqslant 3[/tex]
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_____
On the graph, solutions correspond to values of x where the red line is in the blue region. (There are none.)
This is a priority! The equation of a parabola is 1/16 (y+3)^=x+4 what are the coordinates of the focus?
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1. You have the following equation of a parabola:
1/16(y+3)^2=x+4
2. Rewriting the equation of the parabola, you have:
(y+3)^2=16(x+4)
3. The vertex of the parabola is:
(h,k)=(-4,-3)
3. Now, you must find the coefficient of the unsquared part, as below:
4p=16
p=16/4
p=4
4. As you can see, the y part is squared and p is positive. This means that the parabola that opens to the right.
5. The focus of the parabola has to be 4 units to the right of the vertex. Therefore, the focus is:
(0,-3)
The answer is: (0,-3)
A collection of dimes and quarters worth $9.25. There are 46 coins in all. Find how many of each there are. How many dimes are there?
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0.10d +0.25(46 -d) = 9.25
-0.15d = 9.25 -(0.25*46) = -2.25 . . . . simplify, subtract .25*46
d = 2.25/.15 = 15 . . . . . . . . . . . . . . . . . divide by the coefficient of d
There are 15 dimes.
Victor Malala has a net income of $1240.00 per month. If he spends $150.00 on food, $244.00 on a car payment, $300.00 on rent, and $ 50.00 on savings, what percent of his net income can he spend on other things?
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Food: F=$150.00
Car payment: C=$244.00
Rent: R=$300.00
Saving: S=$50.00
Other things: O=?
F+C+R+S+O=I
$150.00+$244.00+$300.00+$50.00+O=$1240.00
Solving for O:
$744.00+O=$1240.00
$744.00+O-$744.00=$1240.00-$744.00
O=$496.00
Percent of his net income Victor can spend on other things: P=?
P=(O/I)*100%
P=($496.00/$1240.00)*100%
P=(0.40)*100%
P=40%
Answer: 40% of his net income Victor can spend on other things.
HELP FAST ILL MAKE BRAINIEST Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following colored data tables. Purple: Weight of elk antler pairs at Mount St Helens NVM: {34, 34, 30, 30, 30, 28, 28, 26} Red: Weight of elk antler pairs at Rocky Mountain NP: {40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the following for each set of data: a. Purple Mean: b. Red Mean: c. Purple Median: d. Red Median: e. Purple MAD: f. Red MAD:
(c) Calculate the means-to-MAD ratio for the two areas of collection. (
d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain. Answer:
Answers
The diagram is shown in figure 1.
a.2 Weight of elk antler pairs at Rocky Mountain NP
The diagram is shown in figure 2.
b. Calculate the following for each set of data:
We can found the mean (µ) of a set of data points by adding them up and dividing by the number of data points.
b.1 Purple Mean:
Set: [tex]\{34, 34, 30, 30, 30, 28, 28, 26\} \rightarrow \frac{34+34+30+30+30+28+28+26}{8} \rightarrow \boxed{\mu=30}[/tex]
b2. Red Mean:
Set: [tex]\{40, 38, 36, 36, 36, 36, 34, 32\} \rightarrow \frac{40+38+36+36+36+36+34+32}{8} \rightarrow \boxed{\mu=36}[/tex]
b.3 Red Median
The Median is the middle of a sorted list of numbers. The median of a finite list of numbers can be found by arranging all the numbers from smallest to greatest. So, arranging the red set we have:
[tex]\{32, 34, 36, 36, 36, 36, 38, 40\}[/tex]
Given that the number of elements is pair, the median can be solved as follows:
[tex]\overline{x}=\frac{x_{(n/2)}+ x_{((n/2)+1)}}{2}[/tex]
∴ [tex]n=8[/tex]
∴ [tex]x_{(n/2)}=x_{(4)}=36[/tex]
∴ [tex]x_{((n/2)+1)}=x_{(5)}=36[/tex]
Then:
[tex]\overline{x}=\frac{36+36}{2}=36[/tex]
b.4 Purple MAD
The Mean Absolute Deviation (MAD) is when you find the distance of each data point from the mean and then find the mean of those distances. So:
[tex]\{34, 34, 30, 30, 30, 28, 28, 26\}[/tex] has [tex]\mu=30[/tex]
[tex]distances=\{4, 4, 0, 0, 0, 2, 2, 4\} \rightarrow \frac{4+4+0+0+0+2+2+4}{8}= \boxed{MAD=2}[/tex]
b.5 Red MAD
[tex]\{40, 38, 36, 36, 36, 36, 34, 32\}[/tex] has [tex]\mu=36[/tex]
[tex]distances=\{4, 2, 0, 0, 0, 0, 2, 4\} \rightarrow \frac{4+2+0+0+0+0+2+4}{8}= \boxed{MAD=1.5}[/tex]
c. Calculate the means-to-MAD ratio for the two areas of collection
c.1 Purple set:
The ratio is the relationship between the mean and the MAD indicating how many times the first number contains the second, so:
[tex]\frac{\mu}{MAD}= \frac{30}{2}=\boxed{15}[/tex]
c.2 Red set:
[tex]\frac{\mu}{MAD}= \frac{36}{1.5}=\boxed{24}[/tex]
d. What inference can be made about the areas in regard to weight of dropped elk antlers?
MAD tells us how far, on average, all values are from the middle. So, in the example weight of elk antler pairs at Mount St Helens NVM are, on average, 2 away from the middle. On the other hand, weight of elk antler pairs at Rocky Mountain NP are, on average, 1.5 away from the middle. So, we can assure that elk antler pairs at Rocky Mountain NP weighs more than elk antler pairs at Mount St Helens NVM.
all real cube roots of 27
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Which of these points does not change its location when it is reflected across the y-axis? (2, 0) (0, 6) (3, 3) (–5, 5)
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Answer:
-5,5
Step-by-step explanation:
Two people started from the same point at the same time and traveled in opposite directions. One traveled at 60 mph and the other at 50 mph. How long will it take before the two people are 440 miles apart?
Answers
x = hours
60x + 50x = 440
110x = 440
110x / 110 = 440/110 = 4
It will take 4 hours
60x+ 50x = 440
60(4) + 50(4) = 440
440 = 440
A triangle has side lengths of 7, 24, and 26. Is the triangle right, acute, or obtuse? a. right c. obtuse b. acute Please select the best answer from the choices provided A B C
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Answer:
Option C. Obtuse
Step-by-step explanation:
we know that
Applying the Pythagoras Theorem
If [tex]c^{2}=a^{2} +b^{2}[/tex] ----> is a right triangle
If [tex]c^{2}>a^{2} +b^{2}[/tex] ----> is a obtuse triangle
If [tex]c^{2}<a^{2} +b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
Verify
[tex]c^{2}=26^{2}= 676[/tex]
[tex]a^{2} +b^{2}=7^{2} +24^{2}=625[/tex]
therefore
[tex]676>625[/tex]
[tex]c^{2}>a^{2} +b^{2}[/tex] -----> is a obtuse triangle
in the sport competition France won more gold medals than Italy, who won more good medals than Korea. if the total number of gold medals won by the consecutive intergers whose sum is 36. find the number of gold medals won by each.
Answers
10+11+12 =33 so the numbers are correct.
France 16
Italy 15
Korea 14
A cylindrical can of cat food has a diameter of 3.5 inches and a height of 1.25 inches. A second brand of cat food is packaged in a cylindrical can with a radius of 1.2 inches and a height of 1.25 inches. What is the difference between the volumes of the cans? Show your work.
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hey can you please help me posted picture of question
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A horizontal shift is indicated by addition/subtraction to x rather than the function.
A right shift is indicated by subtracting the number from x. So a right shift of F(x) will be indicated by F(x-2)
Thus,
G(x) = F(x-2)
G(x) = (x-2)²
So, the answer to this question is option B
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of .) 452.16 cm3 840.54 cm3 1,055.04 cm3 1,456.96 cm3 NextReset
Answers
So,
Volume of air = Volume of cylinder - Volume of cone
[tex]= \pi r^{2}h- \frac{1}{3} \pi r^{2}h \\ \\ =3.14(5)^{2}(16)- \frac{1}{3}(3.14) (4)^{2}(12) \\ \\ =1055.04[/tex]
Thus, the volume of the air surrounding the cone and inside the cylinder will be 1055.04 cubic centimeter
cylinder = pi * r * r * h
cone = pi * r * r * h/3
substitute the values;
The volume of air is equal to 1055.05cu.cm
The price of a pair of jeans at a store increased by 25% to $40. Find the price of the pair of jeans before the increase
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25&=0.25
0.25x40=10
Now all you gotta do it’s
40-10=30
You subtract becaus le they ask you to find the price before it was increased so that why you gotta subrtract it
The polar coordinates of a point are given. find the rectangular coordinates of this point.(5, 3pi/4
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Here, x is 5cos 135 deg = 5(-1/sqrt(3))
and y is 5* sin 135 deg = 5*(1/sqrt(3))
Write this point in the form (x,y), using the above values for x and y.
Tangerine trees yield 50 pounds of fruit per acre and grapefruit trees yield 75 pounds of fruit per acre. John's orchard produced a maximum total of 1,500 pounds of fruit. Is it possible for John to have 25 acres of tangerine trees and 15 acres of grapefruit trees?
No, because 50(25) + 75(15) ≠ 1500 No, because (50 + 75)(20 + 15) ≠ 1500 Yes, because 50(25) + 75(15) ≥ 1500 Yes, because 50 + 75 + 25 + 15 ≤ 1500
Answers
Total pounds of trees = 50x + 75y
For x = 25 acres and y = 15 acres
Total weight of trees = 50*25 + 75*15 = 2,375 pounds
This exceeds the maximum weight of fruits (that is, 1,500 pounds) possible from this farm. Therefore, John cannot have 25 acres of Tangerine trees and 15 acres of grapefruit trees.
For his phone service, Jason pays a monthly fee of $19, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $75.10.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answers
Given:
monthly fee - $19
additional - $0.05 per minute
charged in a month - $75.10
Req:
number of minutes
Sol:
monthly fee + additional fee ≥ charged in a month
19 + 0.05m ≥ 75.10
0.05m ≥ 56.10
m ≥ 1,122 minutes per month
Jason used his phone service for 1,112 minutes in the span of one month
for triangle cab find the length of a Side a
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the law of cosines establishes that
a²=c²+b²-2*c*b*cos A
in this problem
a=?
b=21
c=32
A=40°
a²=32²+21²-2*32*21*cos 40-----> a²=435.44---------> a=20.87 units
The numbers of rooms for 15 homes recently sold were: 8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9. what is the sample standard deviation?
Answers
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9
to get the standard deviation we use the formula for variance given by:
σ²=[Σ(x-μ)²]/(n-1)
σ² is the variance
μ is the mean
The mean of the data will be:
μ=(8+8+8+5+9+8+7+6+6+7+7+7+7+9+9)/15=7.4
The variance will be found as follows:
σ²=[(8-7.4)²×4+(5-7.4)²+3×(9-7.4)²+5×(7-7.4)²+2×(6-7.4)²]/(15-1)
σ²=1.4
thus
σ=√1.4=1.1183
Hence, the sample standard deviation is:
1.1832
Step-by-step explanation:The data is given by:
8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9.
The mean of these data points is given by:
[tex]Mean(x')=\dfrac{8+8+8+5+9+8+7+6+6+7+7+7+7+9+9}{15}\\\\i.e.\\\\Mean(x')=\dfrac{111}{15}\\\\i.e.\\\\Mean(x')=7.4[/tex]
Now,
x x-x' (x-x')²
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
8 8-7.4=0.6 0.36
5 5-7.4= -2.4 5.76
9 9-7.4=1.6 2.56
8 8-7.4=0.6 0.36
7 7-7.4= -0.4 0.16
6 6-7.4= -1.4 1.96
6 6-7.4= -1.4 1.96
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
7 7-7.4= -0.4 0.16
9 9-7.4=1.6 2.56
9 9-7.4=1.6 2.56
∑(x-x')²=19.69
Now the variance of the sample population is given by:
[tex]Variance=\dfrac{\sum (x-x')^2}{n-1}[/tex]
where n is the number of data points.
Here n= 15
Hence, n-1=14
Hence, we get:
[tex]Variance=\dfrac{19.6}{14}\\\\i.e.\\\\Variance=1.4[/tex]
We know that the standard deviation is the square root of the variance.
i.e.
[tex]Standard\ deviation=\sqrt{1.4}\\\\i.e.\\\\Standard\ deviation=1.1832[/tex]
If the mean waiting time for the next arrival is 12 minutes, what is the median waiting time? 8.3 minutes 12 minutes 9.1 minutes 7.2 minutes
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Since the mean waiting time is 12 minutes, the median waiting time would also be 12 minutes.
Here's how we can find the median waiting time:
Since the mean waiting time is 12 minutes, it means that if you were to add up all the waiting times of different arrivals and divide by the number of arrivals, you would get 12 minutes.
Now, for the median waiting time, we're looking for the value that falls exactly in the middle of all the waiting times.
If the distribution is symmetrical, which is often the case with waiting times, the mean and median will be the same.
Express Express 0.45 as a percent
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To change 0.45 to a percent, we can move the decimal point 2 places to the right and add the percent sign.
If we move the decimal 2 places to the right, we will end up with 45 and then we will add the percent sign and it will become 45%
Therefore, 0.45 to a percent is 45%
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?
What are the different types of solutions that you can get when you solve a system of linear equations? Describe the graphs of these different types of systems.
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Answer:
there are no solutions (lines do not intersect)there is one solution (lines intersect at one point)there are an infinite number of solutions (lines overlap—are the same line)Step-by-step explanation:
"A system of linear equations" covers a lot of territory. In Algebra 1, it usually means two linear equations in two unknowns. Each of those equations will graph as a line on a coordinate plane.
A solution is a point that satisfies all the equations. That is, it is a point that is on all the lines described by the system of equations.
The geometry of lines on a plane comes into play with regard to solutions.
The lines may be parallel, hence never intersect. (No points will be on all the lines.)The lines may intersect at one point.The lines may be the same line, overlapping, identical, coincident, consisting of all the same points, an infinite number.