Find the interval (s) where f' (x) > 0 for the function f(x) 1+x2 (= 2x (-1,1) 0 (-inf,-1) O (1, inf) None of these
Answers
The interval where f'(x) > 0 is (0, +∞).
- The interval where f(x) is increasing is (-1, 1).
Let's first find the derivative of the function f(x) = 1 + x^2:
f'(x) = d/dx (1 + x^2) = 2x
To find the intervals where f'(x) > 0, we need to find the values of x where 2x > 0. This inequality is true for all x greater than 0, and false for all x less than 0. Therefore, the interval where f'(x) > 0 is:
(0, +∞)
Note that this interval is included in the interval (-1, 1), so we can also say that f(x) is increasing on the interval (-1, 1).
However, it's important to note that the interval where f'(x) > 0 is not the same as the interval where f(x) is increasing. The interval where f(x) is increasing is the open interval (-1, 1), since the function is not defined at x = ±∞.
To summarize:
- The interval where f'(x) > 0 is (0, +∞).
- The interval where f(x) is increasing is (-1, 1).
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Related Questions
Mr.Mcleinis went to the fair and got some food he ordered 5 cakes (f) , 6 tacos(t),and 3 Lemonade's (d)
Mrs.williumms also went to the fair and ordered 3 cakes (f) ,1 turkey leg (L) ,and 2 Lemonade's (d)
Answers
Answer:
20
Step-by-step explanation:
assuming this is addition you have to add 5,6 and 3 that will get you 14 and then you will have to add 3,1 and 2 witch will get you 6 if you add 14 and 6 you will get 20. ps: i hope this helps
14.12 a temperature function is f (x, y) = 2x3y2 − 6xy − x2 3y develop a one-dimensional function in the temperature gradient direction at the point (1, 1).
Answers
The one-dimensional function in the temperature gradient direction at the point (1,1) is: \(g(t) = f(1,1) + D_∇f f(1,1) t = f(1,1) + (416/9) t.\)
How we find the one dimensional function in the temperature?Sure, here are the steps to find the one-dimensional function in the temperature gradient direction at the point (1,1) for the given temperature function \(f(x,y) = 2x^3y^2 − 6xy − x^2/3y:\)
To find the gradient vector of f(x,y) at the point (1,1), we need to compute its partial derivatives with respect to x and y and evaluate them at (1,1):
\(∂f/∂x = 6x^2y - 6y - 2x/3y\)
\(∂f/∂y = 4x^3 - 2x^2/3y^2 - 6x/3y\)
Evaluating these partial derivatives at (1,1), we get:
\(∂f/∂x(1,1) = 6 - 2/3 = 16/3\)
\(∂f/∂y(1,1) = 4 - 2/3 - 2 = 10/3\)
Therefore, the gradient vector of f(x,y) at the point (1,1) is:
\(∇f(1,1) = [16/3, 10/3]\)
To find the one-dimensional function in the temperature gradient direction, we need to compute the directional derivative of f(x,y) in the direction of its gradient at the point (1,1). The directional derivative is given by:
\(D_∇f f(x,y) = ∇f(x,y) · ∇f(x,y)\)
where · denotes the dot product of two vectors.
Plugging in the values of ∇f(1,1), we get:
\(D_∇f f(1,1) = ∇f(1,1) · ∇f(1,1) = [16/3, 10/3] · [16/3, 10/3] = 416/9\)
Therefore, the one-dimensional function in the temperature gradient direction at the point (1,1) is:
\(g(t) = f(1,1) + D_∇f f(1,1) t = f(1,1) + (416/9) t\)
where t is the distance along the direction of the gradient from the point (1,1).
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Based on the angles, this triangle will be identified as a(n)
triangle.
Answers
An art gallery displays a large painting in the center of a wall that is 242424 feet (\text{ft})(ft)left parenthesis, start text, f, t, end text, right parenthesis wide. The painting is 10\,\text{ft}10ft10, start text, f, t, end text wide. Which of the following equations can be used to find the distances, xxx, in feet, from the left end of the wall to the edges of the painting
Answers
The equation that can be used to find the distances from the left end of the wall to the edges of the painting is x = 12 - 5/2 × 10.
The painting is centered on the wall, so the distance from the left end of the wall to the center of the painting is 12 feet. The painting is 10 feet wide, so the distance from the center of the painting to each edge is 5 feet. Therefore, the distance from the left end of the wall to each edge of the painting is 12 feet - 5 feet = 7 feet.
The equation x = 12 - 5/2 × 10 can be used to calculate this distance. The variable x represents the distance from the left end of the wall to the edge of the painting, 12 represents the distance from the left end of the wall to the center of the painting, and 5/2 × 10 represents the distance from the center of the painting to the edge of the painting.
The other equations listed are not correct because they do not take into account the fact that the painting is centered on the wall. The equation x = 10 would be correct if the painting were placed flush against the left end of the wall. The equation x = 24 - 10 would be correct if the painting were placed flush against the right end of the wall.
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A car dealership is offering $1,500 cash back on the
purchase of a new vehicle. The cost, after the cash
back, of a new vehicle can be modeled by the function
C(x) = X – 1,500, where x is the original price of the
vehicle. The vehicle is subject to a sales tax of 8.43%,
so the total price of the vehicle is represented by the
function P(O) = 1.08430.
Answers
Answer:
D- P(C(x)) = 1.0843x – 1,626.45
Step-by-step explanation:
Answer:
D- PC(x)) = 1.0843x – 1,626.45
Step-by-step explanation:
Explain briefly the difference between spot heights and trigonometrical stations or points.
Answers
Answer:
Step-by-step explanation:
A spot height shows exact heights by a black dot with a number next to it. The number is the height above sea level in metres. Trig points or Triangulation Pillars are another way of spotting the top of a mountain on a map
) In unit-vector notation, what is the sum of
a
=(5.2 m)
i
^
+(1.4 m)
j
^
and
b
=(−12.0 m)
i
^
+(6.8 m)
j
^
. What are (b) the magnitude and (c) the direction of
a
+
b
(relative to
i
^
)? (a) Number
i
^
+
j
^
Units (b) Number Units (c) Number Units
Answers
In unit-vector notation, the sum of a= \(5.2 \ \boldsymbol{\hat{i}}+1.4\ \boldsymbol{\hat{j}}\) and b= \(-12.0\ \boldsymbol{\hat{i}}+6.8\ \boldsymbol{\hat{j}}\) is \(-6.8\ \boldsymbol{\hat{i}}+8.2\ \boldsymbol{\hat{j}}\), the magnitude of a+b is 10.65m and the direction of a+b relative to \(\hat{i}\) is \(-50^\circ\).
a) To find the sum of a+b, follow these steps:
In unit-vector notation, the sum of a and b is given by the expression; \({\bf a}+{\bf b}=(5.2 \ \boldsymbol{\hat{i}}+1.4\ \boldsymbol{\hat{j}})+(-12.0\ \boldsymbol{\hat{i}}+6.8\ \boldsymbol{\hat{j}})\\=(5.2-12.0)\ \boldsymbol{\hat{i}}+(1.4+6.8)\ \boldsymbol{\hat{j}}\\=-6.8\ \boldsymbol{\hat{i}}+8.2\ \boldsymbol{\hat{j}}\).Thus, the sum of a and b is \({\bf a}+{\bf b}=-6.8\ \boldsymbol{\hat{i}}+8.2\ \boldsymbol{\hat{j}}\).b) To find the magnitude of a+b, follow these steps:
The magnitude of the sum \({\bf a}+{\bf b}\) is given by;\(|{\bf a}+{\bf b}|=\sqrt{(-6.8)^2+(8.2)^2}=10.65 \ m\). Therefore, the magnitude of \({\bf a}+{\bf b}\) is 10.65m.c) To find the direction of a+b relative to \(\boldsymbol{\hat{i}}\), follow these steps:
The direction of \({\bf a}+{\bf b}\) relative to \(\boldsymbol{\hat{i}}\) is given by \(\theta = \tan^{-1}\left(\frac{8.2}{-6.8}\right)=-50^\circ\). Therefore, the direction of \({\bf a}+{\bf b}\) relative to \(\boldsymbol{\hat{i}}\) is \(-50^\circ\).Learn more about unit-vector notation:
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Find the area of:Inner loop of r=1+2 cos 0 Between the loops of r=1+2 cos 0
Answers
The area of the inner loop of r=1+2 cos 0 is approximately 231.4 square units.
To find the area of the inner loop of r=1+2 cos 0, we need to find the limits of integration first. The inner loop exists between the angles where r=0, which are 60 degrees and 300 degrees, so we will integrate from 60 to 300 degrees.
The area of a polar curve can be found using the formula A = 1/2 ∫[a,b] r^2 dθ. For this problem, the limits of integration are from 60 to 300 degrees, and the function is r=1+2 cos 0. So, the area of the inner loop is:
A = 1/2 ∫[60,300] (1+2cosθ)^2 dθ
Using the double angle formula, 2cos^2θ = 1+cos2θ, we can simplify the integrand to:
A = 1/2 ∫[60,300] (5+4cos2θ) dθ
Integrating this expression gives:
A = 1/2 [5θ + 2sin2θ] evaluated from 60 to 300 degrees
A = 1/2 [5(240) + 2sin(600) - 5(60) - 2sin(120)]
A = 240 - (5/2)√3 ≈ 231.4 square units
Therefore, the area of the inner loop of r=1+2 cos 0 is approximately 231.4 square units. The area between the loops of r=1+2 cos 0 can be found by subtracting the area of the inner loop from the area of the outer loop.
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A magician asks a volunteer to think of two different positive integers without telling her what they are. She then asks him to calculate x, the sum of the larger number with the square of the smaller, and y, the difference between the numbers. The volunteer tells her that x = 9 and y = 3. Find the original numbers.
Answers
Answer:
the original numbers are 5 and 2
Step-by-step explanation:
fistly it says inorder to find x one has to add the larger number to the square of the smaller number. So in this case start off with smaller guesses of positive integers as it is simpler that way.
the first guesses that would end up giving you 9 as an answer is 5 and 2
5+(2×2)=9So now that the integers chosen fit in when calculating x we have to check if it also checks out in calculating y.
For y the difference between the 2 integers have to give an answer of 3. after calculations it the numbers comply to the statement for y;
5-2=3hence the answers are 5 and 2
ASAP, Please help me with this question this is time sensitive.
Erik buys a new combination lock for his locker at the gym. The lock has 3 dials, each with the numbers 0 through 9.
The probability that he sets the combination as 4-3-9 is _____.
Answers
Answer: did anyone find the answer???
Step-by-step explanation:
A data-entry clerk spends $86 per week for food. This is 20% of his weekly income. What is the weekly income? Show work please :
Answers
Answer:
$430
Step-by-step explanation:
Let the weekly income be x
Money spent on food= $86
% of weekly income spent on food = 20
20% of weekly income in terms = 20/100 * x = x/5
This, income is equal to $86 as given
thus,
x/5 = 86
x = 86*5 = 430
Thus, weekly income is $430.
A computer monitor has a width of 14.60 inches and a height of 10.95 inches. What is the area of the monitor display in square meters? area How many significant figures should there be in the answer? 2 3 4 5
Answers
The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.
The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.
The conversion factor from inches to meters is 0.0254 meters per inch.
Width in meters = 14.60 inches * 0.0254 meters/inch
Height in meters = 10.95 inches * 0.0254 meters/inch
Area = Width in meters * Height in meters
We calculate the area:
Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters
Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters
Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters
Now, we determine the number of significant figures.
The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.
Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.
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Help me out with this question (geometry)
Answers
Answer:
m<8=m<4=105
m<4=180-(4x-1)
=180-4x+1
105 =-4x+181
4x= 181-105
4x=76
X=19
m<6=180-105
=75
y-31=75
y =75+31
y=106
X+y=19+106
=125
hi, I NEED HELP.uhh yea i guess
Answers
Answer:
0.61 i did this one to :)
Answer:
Yeah I suppose you do,
Well Model 1 is shaded 23 out of 100, so as a decimal it would be 0.23, and Model 2 is shaded 38 out of 100 so as a decimal it would be 0.38
Now if the decimals were added together the sum would equal
0.61
Step-by-step explanation:
Hope it helped
Please help me! I am so bad at math. 7(6+5x)=3x-22
Answers
42+35x–3x=–22
42+32x=–22
32x=–22–42
32x=–64
x=–64/32
The answer is x= –2
Answer:
-2
Step-by-step explanation:
42+35x=3x-22
35x-3x=-22-42
32x=-64
therefore, x= -64/32
and through further simplification you will get
-2
hope this helped you ( ꈍᴗꈍ)
Please help!! Will give brainiest to the first person who answers
Simplify the expression:
( 4+ 7q) (2)
Answers
Answer: 14q + 8 is the answer
Step-by-step explanation:
Answer:
8 + 14q
Step-by-step explanation:
2 x 4 = 8
2 x 7q = 14q
(8 + 14q)
Hoped it helps! :D
Select all the expressions which are equivalent to –3(0.15 – 0.2 + 0.25p).
A. –0.45 – 0.6 + 0.25p
B. 0.15 – 0.75p
C. 3(0.15 + 0.2 + 0.25p)
D. –3(–0.05 + 0.25p)
E. –3(0.05 + 0.25p)
I need help ASAP.
Answers
Answer:
–3(0.15 – 0.2 + 0.25p) is equivalent to –3(-0.05 + 0.25p) and 0.15 – 0.75p
Rivika used the last four digits of her telephone number,1048, followed by its prime factorization to create her email password Determine her password
Answers
Answer: I'm pretty sure I can help, just give me like 3 minutes..
-Angie
Answer:
Her password is 1048222131.
Like Angie said, 1048 * 2* 2 * 2 * 131.
But before that you need to decompose 1048 into its prime factors.
The Prime Factorization is:
2 x 2 x 2 x 131
In Exponential Form:
23 x 1311
CSV Format:
2, 2, 2, 131
All Factors of 1048:
1, 2, 4, 8, 131, 262, 524, 1048
Prime Factors Tree
1048
/ \
2 524
/ \
2 262
/ \
2 131
There you go! If you need more help just reach out to me!
imagine that you are a researcher conducting a survey for a client. you are trying to decide what sample size you need. what would the main advantage be of a larger sample size?
Answers
Large sample size gives more accurate information about population.
The main advantages of Large sample size is :
1. Large sample size provide stronger and more reliable information about parent population.
2. It will help researcher to capture outliers and sweeping out in sample.
3. Measuring large sample size allows one to divide the sample into segments .
4. Large sample size helps in obtaining a quality and precise mean .
Some disadvantages of Large sample size is :
1. Large sample size will be time consuming and more expensive to work with
2. It require higher financial involvement to complete the survey.
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find the slope of the line
Answers
Answer:
The slope of the line is 1
Step-by-step explanation:
I picked two points on the line: (0,3) and (-3,0). Then, I used the formula for slope which is the change in y over the change in x and got the answer 1.
Explain why, if A and B are sets, it is not necessarily true that n(A - B) = n(A) - n(B). Give counterexample.
Answers
It is not necessarily true that n(A - B) = n(A) - n(B) when A and B are sets.
What is an example that shows n(A - B) ≠ n(A) - n(B) when A and B are sets?Consider two sets, A = {1, 2, 3} and B = {1, 4}.
In this case, A - B = {2, 3}, n(A) = 3, n(B) = 2, and n(A - B) = 2. Therefore, n(A - B) ≠ n(A) - n(B).
In set theory, the difference of two sets A and B is defined as the set of elements in A that are not in B. The cardinality of a set is the number of elements it contains.
The equation n(A - B) = n(A) - n(B) is not always true, and there exist counterexamples where it does not hold. One such counterexample is A = {1, 2, 3} and B = {1, 4}. In this case, A - B = {2, 3}, n(A) = 3, n(B) = 2, and n(A - B) = 2. Thus, n(A - B) ≠ n(A) - n(B).
It is important to note that the equation n(A - B) = n(A) - n(B) holds only when every element in A - B is also in A and not in B. If this condition is not met, the equation does not hold.
Therefore, one must be cautious when applying this equation and ensure that all elements are properly accounted for.
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9) If point B with coordinates (5, 2) is dilated by a scale factor of 3, what will be the coordinates of the image point B'?
Answers
Answer
Option A is correct.
B' (15, 6) is the answer.
Explanation
To dilate a given coordinate (x, y) about the origin by a scale factor of n, we will obtain (nx, ny).
So, for the given coordinate (5, 2), dilating by the scale factor of 3, we will obtain
B (5, 2) = B' (5×3, 2×3) = B' (15, 6)
Hope this Helps!!!
2/3 (m-1/2) +3= m/3-7 Please Explain (Will give brainliest)
Answers
Answer:
m= -29
Step-by-step explanation:
This is a bit of a complex equation, but let's work through it.
2/3 (m-1/2) +3= m/3-7
First, we need to distribute the 2/3.
(2/3)(m)+(2/3)(−1/2)+3=m/3+−7
Now we simplify that.
2/3m+−1/3+3=1/3m+−7
We can now combine like terms.
2/3m+8/3=1/3m+−7
The goal is to isolate the variable, so we should subtract 1/3m from both sides.
1/3m+8/3=−7
Lets keep going! We can subtract 8/3 from both sides.
1/3m=-29/3
Well now we know what 1/3 of m is, but we want to know what m is. So we can multiply both sides by three to finally find out what m is!
m=-29
We did it! m=-29
yeah i’m really not sure what the answer is to this one
Answers
SA = 62
V = 30
which whould most likely weigh 2 pounds
a mouse
a pencil
a dictionary
a school desk
Answers
Answer: I say a dictionary.
Step-by-step explanation:
A pencil wouldn’t weight 2 pounds so that’s the only logical answer to me
Solve the equation -16(d+1) = -20.
Answers
Answer:
\(d=\frac{1}{4}\)
Step-by-step explanation:
\(-16(d+1)=-20\) (given)
\(-16d-16=-20\) (expand the brackets)
\(-16d=-4\)
\(d=\frac{1}{4}\)
Hope this helps :)
Answer:
d = 1/4
Step-by-step explanation:
- 16 (d + 1) = - 20
- 16d - 16 = - 20
- 16d = -20 + 16
- 16d = - 4
d = \(\frac{-4}{-16}\)
d = \(\frac{1}{4}\)
Marty bought a piece of material that was 68 yard long and a piece that was 48 yard long. Which statement is TRUE? A. 48> 68 B. 68< 48 C. 68> 48 D. 48= 68
Answers
Answer:
C
Step-by-step explanation:
68 is bigger than 48...
Consider w = 2(cos(210°) + isin(210°)) and z = 2(cos(330°) + isin(330°)). What is w- z expressed in rectangular
form?
2i
-2i
-2 3+ 0i
-2 /3-2i
Answers
Answer:
C
Step-by-step explanation:
right on edge
The value of the expression w - z for the given complex number will be -2√3 + 0i thus option (C) will be correct.
What is a complex number?Complex numbers are helpful in finding the square root of negative numbers.
A complex number is the sum of a real number and an imaginary number.
If we solve x² + 1 = 0 ⇒ x = √(-1) which is called as iota(i).
As per the given complex numbers,
w = 2(cos(210°) + isin(210°))
w = 2(-√3/2 + i(-1/2)]
w = -√3 - i
z = 2[cos(330°) + isin(330°)]
z = 2[√3/2 + i(-1/2)
z = √3 - i
Now, w - z will be as,
w - z = (-√3 - i) - (√3 - i)
w - z = -√3 - √3 - i + i
w - z = -2√3 + 0 i
Hence "The value of the expression w - z for the given complex number will be -2√3 + 0i".
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Teresa says she stacks about 7 dishes by hand every minute.
What line represents Teresa’s statement?
A. Line a
B. Line b
C. Line c
D. Line d
Answers
Answer:
line D
Step-by-step explanation:
implify without calculator: 92-√36 x 3V1000 (Show all calculations)
Answers
92-√36 ×3√1000
92-√6^2 ×3√10^3
92-6×3×10√10
92-6×30√10
86×30√10
2580√10