Answers
Answer: Choice D)
(-1.5, -1) and (0, 1)
=============================================================
Explanation:
Exponents can be a bit clunky if you have too many of them, and if they're nested like this. Writing something like e^(x^2) may seem confusing if you aren't careful. I'm going to use a different notation approach. I'll use "exp" notation instead.
So instead of writing something like e^(x^2), I'll write exp(x^2).
The given derivative is
f ' (x) = exp(x^4-2x^2+1) - 2
and this only applies when -1.5 < x < 1.5
Apply the derivative to both sides and we'll find the second derivative
f ' (x) = exp(x^4-2x^2+1) - 2
f '' (x) = d/dx[ exp(x^4-2x^2+1) - 2 ]
f '' (x) = exp(x^4-2x^2+1)*d/dx[ x^4-2x^2+1 ]
f '' (x) = exp(x^4-2x^2+1)*(4x^3-4x)
f '' (x) = (4x^3-4x)*exp(x^4-2x^2+1)
From here, we need to find the roots of f '' (x).
Set f '' (x) equal to zero and solve to get...
f '' (x) = 0
(4x^3-4x)*exp(x^4-2x^2+1) = 0
4x^3-4x = 0 ..... or .... exp(x^4-2x^2+1) = 0
4x(x^2-1) = 0
4x(x+1)(x-1) = 0
4x = 0 or x+1 = 0 or x-1 = 0
x = 0 or x = -1 or x = 1
Those are the three roots. We ignore the equation exp(x^4-2x^2+1) = 0 because it doesn't have any real number solutions.
---------------------
The three roots of x = 0 or x = -1 or x = 1 represent possible locations of points of inflection (POI). Recall that a POI is where the function changes concavity. To determine if we have a POI or not, we'll need to a sign test.
Draw out a number line. Plot -1, 0, and 1 in that order on it. Pick something to the left of -1 but larger than -1.5, lets say we pick x = -1.2. Plugging this into the second derivative function leads to...
f '' (x) = (4x^3-4x)*exp(x^4-2x^2+1)
f '' (-1.2) = (4(-1.2)^3-4(-1.2))*exp((-1.2)^4-2(-1.2)^2+1)
f '' (-1.2) = -2.563
That value is approximate. The actual value itself doesn't matter. What does matter is the sign of the result. The negative second derivative value tells us we have a concave down region. So we just found that f(x) is concave down for the interval -1.5 < x < -1, which converts to the interval notation (-1.5, -1)
Repeat the process for something between x = -1 and x = 0. I'll pick x = -0.5 and it leads to f '' (-0.5) = 2.63 approximately. The positive result tells us that we have a concave up region. Therefore, -1 < x < 0 is not part of the answer we're after.
Repeat for something between x = 0 and x = 1. I'll pick x = 0.5 and it produces f '' (0.5) = -2.63 approximately. So the region 0 < x < 1 is also concave down. Meaning that the interval notation (0,1) is also part of the answer.
So far we have the interval notation of (-1.5, -1) and (0,1) as part of our solution set.
Lastly, we need to check something to the right of x = 1, but smaller than 1.5; let's go for x = 1.2
You should find that f '' (1.2) = 2.563 which allows us to rule out the region on the interval 1 < x < 1.5
Overall, the final answer is (-1.5, -1) and (0, 1)
Related Questions
Activity 4:
roup
Evaluate 2x + 5 if:
1. X=5
2. X=4
3. X=-7
4. x = 0
5. x= 13
please anwer it
Answers
Answer:
1. 15
2. 13
3. -9
4. 5
5. 31
just put the values in the given equation.
:)
Determine the value of x
ASAP! Help!
Answers
Answer:
Step-by-step explanation:
B
90/20=4.5
Guys can you help me please :( ASAP
Answers
Answer:
The answer is 25 + 11
Step-by-step explanation:
Hope this helps
(1,4) (2,7) (3,10) (4,13) find the equation in slope-intercept form.
Answers
Answer:
y = 3x + 1
Step-by-step explanation:
The way you find slope is change in y over change in x, (as a fraction).
So then your equation is y = 3x because the y value goes up 3 times and the x goes up once (3/1), and then you see what value y has when x = 0 to find the b value, which is one.
Please please help!!!!
Answers
Answer:
7 and 1/4
Step-by-step explanation:
Answer:
The answer is 7 1/4 or 29/4
Step-by-step explanation:
List the following from least to greatest: 3, -4, 0, 1, -9
Answers
Answer:
Step-by-step explanation:
-9,-4,0,1,3
Answer: From least to greatest. = -9, -4, 0, 1, 3.
PLEASE HELP THIS IS VERY IMPORTANT I'LL GIVE YOU BRAIN THING IF ITS CORRECT!! <3 NO LINKS PLEASEE.
Answers
Answer:
a is 23 1/24 or 553/24 and b is 109 43/87
Step-by-step explanation:
5 equivalent fractions of 4/8
Answers
Answer:
2/4 1/2 5/10 6/12 10/20
Step-by-step explanation:
just pick an even denominator and take half of that number for the numerator. This only works because the most basic form of 4/8 is 1/2. This method only works if your selected fraction is equivalent to 1/2.
2/4
6/12
12/24
50/100
Basically any number that can split evenly like 4/8
What is the range of the data Colin collected?
Answers
Answer:
5
Step-by-step explanation:
5. Write in Polar form the following complex numbers
(a) 4+6j
Answers
Answer:
https://www.wolframalpha.com/widgets/view.jsp?id=ecc4c3ee7c6b1f12d078f6541a983c2d
use that it will give you a step by step answer.
CARD #8: Henry says that the two figures will be congruent. A figure on a coordinate plane is dilated by a scale factor that is less than one. Heather says that the two figures will be similar.
Answers
Answer:
Heather is correct.
Step-by-step explanation:
Two figures are similar if the figures have the same shape but different size
Two figures are congruent if they have the same shape and size.
So, if we dilate a given figure (by any factor different than one) then we are changing the size of this figure.
Finally, a figure and its dilation can't be congruent, as these figures have different size (but still have the same shape, so the figures are always similar)
Then Heather is correct.
True or False
Two major composers of minimalism include Steve Reich and John Cage.
A. true
B. false
Sorry for the wrong subject
Answers
Answer:
false
Step-by-step explanation:
:)))))))))))))))))
Three factories produce light bulbs to supply the market. Factory A produces 40%, 20% of the tools are produced in factory B and 40% in factory C. 5% of the bulbs produced in factory A, 3% of the bulbs produced in factory B and 4% of the bulbs produced in factory C are defective.A bulb is selected at random in the market and found to be defective. What is the probability that this bulb was produced by factory A?
Answers
Answer:
0.4762 = 47.62% probability that this bulb was produced by factory A
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Bulb is defective.
Event B: Produced by factory A.
Probability of a bulb being defective.
5% of 40%(factory A)
3% of 20%(factory B)
4% of 40%(factory C). So
[tex]P(A) = 0.05*0.4 + 0.03*0.2 + 0.04*0.4 = 0.042[/tex]
Defective and from factory A:
5% of 40%. So
[tex]P(A \cap B) = 0.05*0.4 = 0.02[/tex]
What is the probability that this bulb was produced by factory A?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.02}{0.042} = 0.4762[/tex]
0.4762 = 47.62% probability that this bulb was produced by factory A
Find the measure of a 3.
ts
43
90°
<<
43 = [?]
Answers
The correct answer is 90
What is the volume of a sphere with a radius
of 6?
A 721
14471
2161
IN 288rt
Answers
Answer:
the volume is 904.32. that guy I don't know what
A 721
14471
IN 288rt
means
calculate the gross margin if the selling price is $264 and the cost is $214
Answers
Answer:
Gross margin= $50
Step-by-step explanation:
Giving the following information:
Selling price= $264
Unitary cost= $214
To calculate the gross margin, we need to deduct from the selling price the unitary cost:
Gross margin= selling price - unitary cost
Gross margin= 264 - 214
Gross margin= $50
Four boxes of cookies were sold to a family of five.each box contains 12 cookies if each family member ate 2 cookies from each box what fraction of the original number of cookies is left?
Answers
First lets find the total number of cookies
12*4=48
48 cookies
Number of cookies eaten
5*2=10
10 were eaten
Cookies left
48-10=38
38/48=19/24
19/24 of the cookies are left
Answer:
38 are left
Step-by-step explanation:
Which one A B C or D?
Answers
Answer:
Step-by-step explanation:
D
Answer:
D
Step-by-step explanation:
5 + 0.55x = 10 + 0.75x pls help and explain
Answers
Step-by-step explanation:
hope it is helpful to you
X = -25
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
0.55x + 5 = 0.75x + 10
Step 2: Subtract 0.75x from both sides.
0.55x + 5 − 0.75x = 0.75x + 10 − 0.75x
−0.2x + 5 = 10
Step 3: Subtract 5 from both sides.
−0.2x + 5 − 5 = 10 − 5
−0.2x = 5
Step 4: Divide both sides by -0.2.
−0.2x/−0.2 = 5/−0.2
x = −25
Find the volumes of the solids whose bases are bounded by the circle x^2 + y^2 = 9, with the indicated cross sections taken perpendicular to the x-axis.
a) Squares
Answers
x ^2 + y ^2 = 9 => y = y(x) = ± √(9 - x ^2)
Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by y(x), which is
√(9 - x ^2) - (- √(9 - x ^2)) = 2 √(9 - x ^2)
The area of each square section is the square of this length,
(2 √(9 - x ^2)) = 4 (9 - x ^2) = 36 - 4x ^2
We get the whole solid for -3 ≤ x ≤ 3, so integrating gives a volume of
[tex]\displaystyle\int_{-3}^3(36-4x^2)\,\mathrm dx=\boxed{144}[/tex]
28÷7×1/4
no links pls
Answers
Answer:
1 is the answer
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
first, you divide 28 by 7 and get 4, then multiply 4 by 1 which is 4, finally divide 4 from 4 with is 1
((28/7)*1)/4=1
What is an angle?
A. part of a line that has two endpoints
ОО
B. part of a line that has one endpoint
C. two rays that have the same endpoint
O O
D. two rays that have the same length
Answers
Answer:
A .part of a line that has two end points
The square of an integer is 5 more than 4 times the integer. Find the integer.
Answers
Answer:
The integer can be -1 or 5.
Step-by-step explanation:
Let an integer is x.
ATQ,
The square of an integer is 5 more than 4 times the integer.
[tex]x^2=5+4x[/tex]
or
[tex]x^2-5-4x=0\\\\x^2-4x-5=0[/tex]
It is a quadratic equation. Using middle term splitting,
[tex]x^2-5x+x-5=0\\\\x(x-5)+1(x-5)=0\\\\(x+1)(x-5)=0\\\\x=-1,5[/tex]
So, the integer can be -1 or 5.
If the square of an integer is 5 more than 4 times the integer, the integers are -1 and 5
Let the unkown integer be "x"
The square of an integer is expressed as x^2
5 more than 4 times the integer is expressed as [tex]4x +5[/tex]
Equate both expressions to have:
[tex]x^2 = 4x + 5\\[/tex]
Equate to zero and factorize:
x^2 - 4x - 5 = 0
x^2 - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x + 1)(x - 5) = 0
x = -1 and 5
Hence the integers are -1 and 5
Leearn more here: https://brainly.com/question/13805464
The list shows the amount of snow, in inches, that fell each day for 5 days.
8, 3, 12, 1,1
What is the mean daily snowfall?
O A. 1 inch
B. 3 inches
OC, 4 inches
D. 5 inches
Answers
Answer:
5 inches
Step-by-step explanation:
add all them and divide by 5.
Astronomers classified the planets into six sizes with five atmosphere types and four average temperature ranges. How many different planet types are there?
Answers
The fraction 5/8
produces a repeating decimal.
___
0.625
True or False
Answers
Answer:
False i just did it
Step-by-step explanation:
What is the least natural number that is greater than 10 and has a remainder of 5 when divided by 6, has a remainder of 5 when divided by 9, and has a remainder of 5 when divided by 12?
Answers
Answer:
41
Step-by-step explanation:
I am essentially going through every multiply of 12 and then adding 5 to it, because we are using the rule that it should have a remainder of 5. It should also be a remainder of 5 if divided by 6 and 9 as well.
12 + 5 = 17
17/6 = 2 R 5
17/9 = 1 R 8
24 + 5 = 29
29/6 = 4 R 5
29/ 9 = 3 R 2
36 + 9 = 41
41/6 = 6 R 5
41/9 = 4 R 5
Hence, the number is 41
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
Step-by-step explanation6:
There are 500 students in school. 40% of them are boys and the rest are girls. What is the percentage of girls? And find the number of boys and number of girls in the school
Answers
? = 60%
500 = 100%
then cross multiply, 500 * 60 is 30,000, divided by 100 is 300, there are 300 girls and 200 boys in the school. the percentage of girls is 60%
PLS DUE RN
WILL GIVE
BRAINLIST
Answers
Answer:
44 in.
Step-by-step explanation:
3 ft 8 in.
1 ft = 12 in.
3 ft = 36 in.
36 in. 8 in.
44 in.
A state in the United States has 193,116 residents living in 22 countries.
[tex]\frac{1}{y} :\frac{22}{193,116}[/tex]
y · 22 = 1 · 193,116
22y = 193,116
22y ÷ 22 = 193,116 ÷ 22
y = 8778
The rate is 8778.
Which expression is equivalent to StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot? Assume y not-equals 0.
Answers
" StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot "is
(X^7/2)(y^-3/5) which is expressed as Option A (x Superscript two-sevenths Baseline) (y Superscript negative three-fifths Baseline)
This is further explained below.
What is an expression?Generally, An expression, often known as a mathematical expression, is a finite collection of symbols that is well-formed according to principles that are dependent on the context in which the expression is being used.
In conclusion, The expression equivalent to StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot is
(X^7/2)(y^-3/5) hence (x Superscript two-sevenths Baseline) (y Superscript negative three-fifths Baseline) Option A.
Read more about expression
https://brainly.com/question/14083225
#SPJ1
CQ
Which expression is equivalent to StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot?
Assume y not-equals 0. (x Superscript two-sevenths Baseline) (y Superscript negative three-fifths Baseline) (x Superscript two-sevenths Baseline) (y Superscript five-thirds Baseline) (x Superscript two-sevenths Baseline) (y Superscript three-fifths Baseline) (x Superscript seven-halves Baseline) (y Superscript negative five-thirds Baseline).
Answer:
A
Step-by-step explanation: