1. Use the following table to answer the questions: (Note: f(x) is a continuous function)
[x] -2,3,4,8
[f(x)] 7, -2, 3, 6
[f'(x)]-4.5,-0.25,1,8
a. If g(x)=f(x), is g(x) a function?
b. Find f(g(4)).
c. Write the equation of the line tangent to g at x = -2.
PLEASE SEE PHOTO! Can you explain why my answers were wrong and can you find the correct answers to all of them?
![1. Use The Following Table To Answer The Questions: (Note: F(x) Is A Continuous Function)[x] -2,3,4,8[f(x)]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/HghD9TkU48zLB5hIDpl3YUTKe9bvDz5s.png)
Answers
1. a. No, g(x) is not a function because f(x) is not invertible. This is because it's not a monotonic function, which we gather from the table. On the interval [-2, 3], f(x) decreases from 7 to -2, but on the following interval [3, 4], f(x) increases to 3 and becomes positive once more. At best, f(x) is locally invertible.
1. b. This is impossible to determine... We can't know g(4) without knowing for which x we have f(x) = 4, but that's not included in the table.
1. c. The slope of the tangent line to f(x) at x = -2 is f'(-2) = -4.5. Then the equation of the tangent to f(x) at x = -2 - which means it passes through the point (-2, f(-2)) = (-2, 7) - is
y - 7 = -4.5 (x - (-2)) ⇒ y = -4.5x + 16
2. Given f(x) = arctan(3x) - ln(1 + 9x²), compute the derivative:
f'(x) = 3/(1 + (3x)²) - 18x/(1 + 9x²)
f'(x) = (3 - 18x)/(1 + 9x²)
Find the critical points of f(x), where f'(x) = 0 or doesn't exist. Only the first case can happen since the denominator is never zero. So
3 - 18x = 0 ⇒ x = 1/6
is the only critical point.
Also compute the second derivative, then check its sign at the critical point:
f''(x) = (-18 - 54x + 162x²) / (1 + 9x²)²
f''(1/6) = -72/5 < 0
The negative sign indicates that x = 1/6 is the site of a local maximum of
f(1/6) = arctan(1/2) - ln(5/4) ≈ 0.241
Also check the values of f(x) at the endpoints of the interval [0, 1]:
f(0) = 0
f(1) = arctan(3) - ln(10) ≈ -1.054
So, the maximum value of f(x) on [0, 1] is f(1/6) ≈ 0.241.
Related Questions
Which equation can we use to find the length of the side labeled x?
Answers
Answer:
(D) sIn(30°) = 5/x
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between sides and trig functions for a right triangle. Here, the hypotenuse and the side opposite the angle are marked. The relevant relationship is ...
Sin = Opposite/Hypotenuse
Filling in figure values, we have ...
sIn(30°) = 5/x
Function g can be thought of as a translated (shifted) version of f(x) = x2.
Write the equation for g(2).
g(x)=
Answers
If the function f(x) is translated at a point (2, 6). Then the function g(x) will be given as g(x) = (x - 2)² + 6.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Function g can be thought of as a translated (shifted) version of f(x) = x².
Then the equation of the function g(x) will be
g(x) = (x - 2)² + 6
Learn more about transforming functions here:
https://brainly.com/question/17006186
#SPJ1
Ryder found the volume of the figure below by using the steps shown. A rectangular prism with a length of 40 millimeters, width of 30 millimeters, and height of 5 millimeters. A rectangular pyramid with a base of 30 millimeters by 40 millimeters and a height of 95 millimeters. Total Volume = B h + one-half B h Equals 5 (40) (3) + one-half (40) (30) (95) Equals 6,000 + 57,000 Equals 63,000 cubic millimeters What mistake, if any, did Ryder make? Ryder determined the volume correctly. Ryder used the wrong formula for the total volume. Ryder used the wrong height for the pyramid. Ryder did not apply the order of operations correctly.
Answers
Answer:
B. Rider used the wrong formula for the total volume.
Step-by-step explanation:
I did the quiz
Answer: B
Step-by-step explanation: I did the quiz, sis, trust me.
4). How many ounces are in 3.5 pounds?
Hint: 16 ounces = 1 pound
3.5
a) 4.6 ounces
19.5 ounces X16
c) 50 ounces
d) 56 ounces
3
Answers
Answer:
there are 56 ounces in 3.5 pounds.
I can’t solve this problem
Answers
Answer:
f(-2) = -8f(-1) = -5f(0) = 0f(1) = 7Step-by-step explanation:
f(w) = [tex]w^{2}[/tex] + 6w
w = -2f(w) = f(-2) = [tex](-2)^{2}[/tex] + 6*(-2) = 4 - 12 = -8
w = -1f(w) = f(-1) = [tex](-1)^{2}[/tex] + 6*(-1) = 1 - 6 = -5
w = 0f(w) = f(0) = [tex]0^{2}[/tex] + 6*0 = 0 + 0 = 0
w = 1f(w) = f(1) = [tex]1^{2}[/tex] + 6*1 = 1 + 6 = 7
Questions in the attached file.
Answers
The area of the triangle based on the information given will be 4 units square
How to calculate the triangle?It should be noted that the area of a triangle is calculated by using the formula:
= 1/2 × base × height
Therefore, the area of the triangle will be:
= 1/2 × base × height
= 1/2 × 2 × 4
= 4 units²
In conclusion, the area of the triangle given will be 4 units square.
Learn more about triangles on:
https://brainly.com/question/17335144
#SPJ1
What is the asymptotes of the graph.
Answers
Answer:
Choice B: x = 2, y = 1.
Step-by-step explanation:
scale drawing of a tree is 4% of the size of the actual tree. The height of the tree in
me drawing is 6 inches. What is the height of the actual tree, in feet?
how your work.
Answers
1. 6
—- = —-
25. X
The reason why we put 6 in the numerator section is because 6 inches is the 4%. After that we know that to get to 6 we need to do 1 x 6 and whatever we do to the top and have to do to the bottom. So 25 x 6 is 150 inches. However the question is saying converting it to feet, and we know that 12 inches is 1 feet. So we do 150 divided by 12 to get 12.5 feet.
Hope this helped!
~Alex
Factor the polynomial 3x – 75
Answers
Answer:
3(x -25)
Step-by-step explanation:
common factor is 3,
75 / 3 = 25
3x / 3 = x
Answer:
3(x-25)
Step-by-step explanation:
The common factor is three
divide both terms by three
3x/3 = x
-75/3 = -25
put them back together with the three outside of the parentheses
3(x-25)
i need help with 7th grade math please 45 points need help ASAP + brainleist
Answers
Answer:
25.13 ft
Step-by-step explanation:
Okay, simple. So first and foremost, set up the equation for the circumference of a circle
Circumference: [tex]2\pi (r)[/tex]
The diameter of the circle is 8 which means the radius is 4
So plug it in
[tex]2\pi (4)[/tex]
That will give us 25.13 ft
I really hope this helps!
Please help me with this
Answers
Lateral SA is 84
Which expression is equivalent to
x^2-1
X^2-x
Answers
Answer:
(x - 1) x - X^2
Hope this helps :)
Find the measure of B
Answers
Answer:
<B = 52°
Step-by-step explanation:
The triangle is 180° Angle A and B add up to 118°
4y° + (3y + 7)° = 112°
7y + 7 = 112°
7y = 105
y = 15
Since you solve for y, plug your y into the angles to solve.
<B = 3y + 7
<B = 3 * 15 + 7
<B = 45 + 7
<B = 52°
Find the distance between points (3,6) and (9,2)
Answers
Answer:
A=(3,6)
B =(9,2)
The distance between AB=√(9-3)^2+(2-6)^2
=3√13
Find the value of x. Round to the nearest 10th.
The area is 34 in²
Answers
Answer:
12
Step-by-step eplanation:
Let the given rhombus be abcd in which ab = bc = cd = da = 20 cm and
ac = 24 cm We know that the diagonals of a rhombus bisect each other at right angles
please help me
Answers
Answer:
384 cm²
Step-by-step explanation:
Property of rhombus :
Diagonals of rhombus bisect each other and are perpendicular to each otherGiven :
Rhombus ABCD and its diagonals AC and BD bisect each other at O AC ⊥ BDAB = BC = CD = DA = 20 cmAC = 24 cmSolving :
Area of the given rhombus is twice the Area of ΔABC formed by the given diagonal and two adjacent sides.
2 × 1/2 × OB × AC24 × OB24 × √AB² - AO²24 × √20² - (AC/2)²24 × √400 - 14424 × √25624 × 16384 cm²
1. Roll a standard die. Amanda wins if the result is prime or 1. Beto wins
if the result is composite
Answers
Answer:
What is the question?
Step-by-step explanation:
prime: 1, 2, 3, 5
composite: 4, 6
Beto has 2/6 = 1/3 chance of winning
Amanda has 4/6 = 2/3 chance of winning
Find the greatest common factor (GCF) for the pair of 12 and 15
Answers
Answer:
3
Step-by-step explanation:
in the image Attached
......
Answer:
3
Step-by-step explanation:
Prime factorize both numbers :
12 = 2² x 315 = 5 x 3The GCF is the highest common term that both terms share.
Hence,
GCF (12, 15) = 3URGANT!!!!
An amount of $17,000 is borrowed for 10 years at 4.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
Answers
Answer:
$27,039
Step-by-step explanation:
Calculating the amount of interest :
A = P (1 + r/n)^(nt)A = interestP = principalr = rate of interest (in decimal)n = number of times compoundedt = time (in years)Given values :
P = $17,000r = 4.75% = 0.0475n = 1t = 10Solving :
A = (17,000)(1 + 0.0475/1)¹⁰A = (17,000)(1.0475)¹⁰A = (17,000)(1.59052433)A = $27,039 (nearest dollar)The ratio of cats to dogs at pet shelter is 4 to 3. if there are 36 dogs, how many cats are there?
A. 27
B. 36
C. 48
D. 52
Answers
calculate the difference between the pairs of numbers below 1 and - 1
Answers
Answer:
we can get the difference by just subtracting -1 and +1 which will give us 0
If anybody could give me the answers
Answers
Answer:
62 Inches
Step-by-step explanation:
It can be seen from the figure.
[tex]{ab}^{2} = {ac}^{2} + {bc}^{2} [/tex]
Pythagoras
AB= 13
So the perimeter is
[tex](13 + 18) \times 2 = 62[/tex]
Find a formula for the nth term
of the arithmetic sequence.
First term 9
Common difference -2
Answers
[tex]n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=9\\ d=-2 \end{cases} \\\\\\ a_n=9+(n-1)(-2)\implies a_n=9-2n+2\implies a_n=11-2n[/tex]
Please help me with this math word problem! Please...
Answers
Let the price of an adult ticket is x and a child ticket is y .
from the question ,
[tex]6x + 2y = 124 \: \: ...(i) \\ \\ 3x + 5y = 100 \: \: ...(ii)[/tex]
Multiply 2 in eq (ii)
[tex]6x + 10y = 200 \: \: ...(iii)[/tex]
On adding eq (iii) and (i)
[tex]6x + 10y = 200 \\ \\ 6x + 2y = 124[/tex]
we get ,
[tex]8y = 76 \\ \\ y = \frac{76}{8} \\ \\ y = 9.5[/tex]
putting y in eq (i)
[tex]6x + 2y = 124 \\ \\ 6x + 2 \times 9.5 = 124 \\ \\ 6x + 19 = 124 \\ \\ 6x = 124 - 19 \\ \\ 6x = 105 \\ \\ x = \frac{105}{6} \\ \\ x = 17.5[/tex]
The value of x = 17.5 and y = 9.5
Hence , The price of an adult ticket is 17.5 and the price of a child ticket is 9.5 .Write the quadratic equation whose roots are 2 and 3, and whose leading coefficient is 3. (Use the letter x to represent the variable.)
Answers
The quadratic equation whose roots are 2 and 3, and whose leading coefficient is 3 will be 3x² - 15x + 18 = 0.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have
Then the quadratic equation whose roots are 2 and 3, and whose leading coefficient is 3.
Then the factor or the quadratic equation will be
(x - 2) and (x - 3)
Then the equation will be
3(x - 2)(x - 3) = 0
3(x² -2x -3x + 6) = 0
3(x² - 5x + 6) = 0
3x² - 15x + 18 = 0
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
#SPJ1
What is the measure of angle 1?
Answers
Answer:
90 degree angle
Step-by-step explanation:
round 18.159 to the nearest tenth
Answers
Answer:
18.2
Step-by-step explanation:
A tenth is the first decimal, on the right of your unit. 5 to the sky (round up) 4 to the floor (round down)
18.159
To find:The nearest tenth of 18.159
Solution:First value right to the decimal place is tenths place. If the value given in hundredths place is 5 or more round up, if not keep it as it is.
So here the value in hundredths place is 5, so we'll have to add 1 to the tenths place.
18.159
= 18.2 ( nearest tenth )
Part 1:
Based on your knowledge of fair decision making and probability concepts, should the Power Pill be produced and distributed? Explain your reasoning.
Part 2:
What effect (if any) did telling two groups about expected outcomes have on results? Use statistics to provide proof for your reasoning and explain.
Part 3:
Are there any flaws in the testing process? Should any of the steps or protocol be changed/avoided during round two of testing? Explain your reasoning.
Answers
The knowledge of fair decision making and probability concepts illustrates that the Power Pill should be produced and distributed.
What is probability?It should be noted that probability simply means the likelihood of the occurence of a particular event.
In this case, the knowledge of fair decision making and probability concepts illustrates that the Power Pill should be produced and distributed.
It's important to adequately carry out a research on the pill and ensure that it's safe.
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
Which of the following is the most significant greenhouse gas due to its long lifespan in the environment?
A. Carbon dioxide
B. Argon dioxide
C. Oxygen
D. Nitrogen Oxide
Answers
I hope that helps.
Answer:
Carbon dioxide
Step-by-step explanation:
I think it’s carbon dioxide because, it is the most significant greenhouse gas. I also think it’s the carbon dioxide because the question is asking which one it is and I chose carbon dioxide.
Which transformations could have occurred to map
ABC to A"B"C?
• a rotation and a reflection
O a translation and a dilation
• a reflection and a dilation
B"
• a dilation and a rotation