Let f be the function defined by f(x) = –x^3 – x. If g represents the inverse of f, what is g′(10)?
Answers
Answer:
[tex]\displaystyle g'(10)=\frac{1}{-13}=-\frac{1}{13}[/tex]
Step-by-step explanation:
The Derivative of the Inverse Function
Let f(x) be a real invertible function, and g(x) the inverse function of f(x), i.e.,:
[tex]g(x)=f^{-1}(x)[/tex]
We can calculate the derivative of the inverse function even if we don't have the inverse function explicitly computed. We use the formula:
[tex]\displaystyle g'(x)=\frac{1}{f'(g(x))}[/tex]
We need to find the value of g'(10) when:
[tex]f(x)=-x^3-x[/tex]
Substituting:
[tex]\displaystyle g'(10)=\frac{1}{f'(g(10))}[/tex]
We don't have the value of g(10) but we can guess its value since the inverse functions f and g satisfy:
if y=f(x), then g(y)=x, thus we need to find a value of x that produces a value of f(x)=10.
We can easily find that x=-2:
[tex]f(-2)=-(-2)^3-(-2)=8+2=10.[/tex]
Thus, g(10)=-2
Now we find:
[tex]f'(x)=-3x^2-1[/tex]
[tex]f'(-2)=-3(-2)^2-1[/tex]
[tex]f'(-2)=-3*4-1=-13[/tex]
Thus, finally:
[tex]\displaystyle g'(10)=\frac{1}{-13}=-\frac{1}{13}[/tex]
Related Questions
What is the simplified form of StartRoot 144 x Superscript 36 Baseline EndRoot?
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Answer:
add pic pls ok?
Step-by-step explanation:
Answer:
Its B 12x^18
Step-by-step explanation:
What variable is used to represent slope?
Answers
[tex]x \: and \: y[/tex]
hope my answer is helpful to you
plz mark me as brainlist
The ordered pairs in the table below represent a linear function.
x
y
2
3
5
9
What is the slope of the function?
Answers
Answer:
The slope is 2
Step-by-step explanation:
Given
x y
2 3
5 9
Required
Determine the slope
First, we have:
[tex](x_1,y_1) = (2,3)[/tex]
[tex](x_2,y_2) = (5,9)[/tex]
The slope is then calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{9-3}{5-2}[/tex]
[tex]m = \frac{6}{3}[/tex]
[tex]m =2[/tex]
Hence, the slope is 2.
Answer:
C
Step-by-step explanation:
Which ordered pair is the best estimate for the solution to the system?
(4.8,5.2)
(5.5,4.3)
(5.1,4.8)
(6.5,5.2)
Answers
Answer:
5.5, 4.333 or 13/3
Step-by-step explanation:
Use substitution method.
Answer:
(5.5, 4.3 )
Step-by-step explanation:
Given the 2 equations
4x - 15y = - 43 → (1)
2x - 3y = - 2 → (2)
Multiplying (2) by - 2 and adding to (1) eliminates the term in x
- 4x + 6y = 4 → (3)
Add (1) and (3) term by term to eliminate x, that is
- 9y = - 39 ( divide both sides by - 9 )
y = [tex]\frac{39}{9}[/tex] ≈ 4.3 ( to 1 dec. place )
Substitute this value into either of the 2 equations and solve for x
Substituting into (2)
2x - 3([tex]\frac{39}{9}[/tex] ) = - 2
2x - 13 = - 2 ( add 13 to both sides )
2x = 11 ( divide both sides by 2 )
x = 5.5
Best solution is (5.5, 4.3 )
The perimeter of a rectangle is 48 cm its length is 4 cm what is the width
Answers
P - 48
w = 20 cm
w − y if w = 20 and y = −8
Answers
Answer:
20 + 8 =28
Step-by-step explanation:
In the given figure, O is the centre of the circle. For
what values of x and y , chord BC will pass through
the centre of circle where points A, B and C are on
the circle?
(a) x = 90, y = 60 (b) x =75,y= 30
(c) x = 65, y = 90 (d) x =90, y = 65
Answers
Answer:
d
Step-by-step explanation:
If chord BC passes through the centre then it is a diameter . then
∠ BAC is the angle in a semicircle and x = 90°
y = 180° - (90 + 25) ← angle sum in a triangle
y = 180° - 115° = 65°
Thus
x = 90°, y = 65° → d
In this exercise we have to use the knowledge of triangles inscribed in a circle, in this way it will be possible to calculate the angles, then:
Letter D
Knowing that it is a triangle inscribed in a circle, in this way we can describe it as:
BAC is the angle in a semicircle and x = 90°Angle sum in a triangle is [tex]y = 180 - (90 + 25)[/tex]So:
[tex]y = 180 - 115 = 65\\ x = 90\\ y = 65 [/tex]
See more about triangles at brainly.com/question/25813512
David bought 3.5 pounds of potatoes for $0.82 per pound. How much did David spend on potatoes?
Answers
plz help me asap i have 7 min plz
Answers
Answer:
[tex] {\huge{\boxed{\red{- 10 < - 4}}}}[/tex]
WILL GIVE BRAINLIEST!!! Help asap :)
Answers
5 2/3 divided by 3/2 please answer soon
Answers
When you divide, multiply by one of the fraction’s reciprocal
17/3 * 2/3 = 34/9
The solution is 34/9
Simplify (30+20)×50 pls find ans
Answers
Answer:
2500
Step-by-step explanation:
solve brackets first
30+20=50
now multiply 50 × 50 (out of the brackets )
50 × 50 = 2500
someone please help i don’t understand
Answers
A cylinder an a cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches.The cone has a radius of 3 inches . What is the height of the Cone?
Answers
Volume of a cone = (1/3) pi x r^2 x h
Volume of a cylinder = pi x r^2 x h
Volume of the cylinder = pi x 2^2 x 3 = 37.68 cubic inches
Now set the volume for the cone to the volume of the cylinder and solve for the height.
37.68 = (1/3) x pi x r^2 x h
37.68 = (1/3) x pi x 3^2 x h
37.68 = (1/3) x pi x 9 x h
37.68 = 9.42 x h
h = 37.68 / 9.42
h = 4
The height of the cone is 4 cm.
Mrs. Robertson is preparing manipulatives for her math class. Each student will receive a plastic cup with 20 two-color counters. The total number of two-color counters, c, that Mrs. Robertson needs varies directly as the number of students, s. Draw a graph showing the proportional relationship between c and s.
Answers
Answer:
Step-by-step explanation:
I just got this correct on the test
The linear relationship between c and s is c = 20s and on the graph paper, it will be a line.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
We have:
Mrs. Robertson is preparing manipulatives for her math class. Each student will receive a plastic cup with 20 two-color counters.
c is the total number of two-color counters
s is the number of students
The linear relationship becomes:
c = 20s
Thus, the linear relationship between c and s is c = 20s and on the graph paper, it will be a line.
Learn more about the proportional here:
brainly.com/question/14263719
#SPJ5
Elena has $225 in her bank account. She takes out $20 each week for weeks. After weeks she has d dollars left in her bank account. Write an equation that represents the amount of money left, d, in her bank account after 5 weeks.
a)20(5)+225=
b)225(5)−20=
c)22520+5=
d)225−20(5)=
.How much money, d, will Elena have in her account after 7 weeks?
Answers
Answer:
the equation to use would be D (255-20(5) = ?). To solve, first multiply 20 and 5 and you would get 100 so the equation would be 255 - 100 = ? Then you would subtract 100 from the 255 to get $155 left. To solve for 7 weeks you would replace the 5 in the equation with 7 so your equation would be 255 - 20(7) = ? Next you would multiply 20 and 7 to get 140. the equation would then be 255 - 140 = ? Subtract 140 from 255 and you would get 115. So after 7 weeks she would have $115 left in her account.
Reciprocal of 5/6=..............
Answers
Step-by-step explanation:
To find the reciprocal, divide 1 by the number given. Simplify. Multiply the numerator by the reciprocal of the denominator. Multiply 65 6 5 by 1 1 .
PLEASE HELP MEEEEEEE
Answers
Answer:
3/4 and in decimal it's 0.75
Step-by-step explanation:
a clothing retailer marks up his merchandise at a rate of 150% so that he can regularly offer a 25% off sale. if the retail price of a sweater is $60 determine the Retailer's cost and the sale price
Answers
Answer:
Answer in photo
Step-by-step explanation:
Find the equation of the linear function represented by the table below in slope intercept form.
Answers
Answer:
y = -3x - 2
Step-by-step explanation:
slope (m) = (-8 - -5) / (2 - 1) ... difference of y/difference of x
m = -3
y = mx + b
y = -3x + b
for (3,-11) b = y + 3x = -11 + 3x3 = -2
equation: y = -3x - 2
PLEASE HELP! WILL MARK BRAINLEIST!!!A local charity is selling seats to a baseball game, Seats cost $20 each and snacks cost an additional $5 each. The charity needs to raise $400 to consider this event a success. graph the linear equation. Be sure to label both axes with the appropriate titles.
Answers
Answer:
I think this should be your answer look at attachment
Step-by-step explanation:
hope this helps
The graph of the given situation is required.
The required graph is attached.
Let x be the cost of each seat
and y be the cost of additional snack.
Cost of seat = $20
Cost of snack = $5
Total cost = $400
The linear equation will be
[tex]20x+5y=400[/tex]
Finding two points
[tex]x=0[/tex]
[tex]5y=400\\\Rightarrow y=\dfrac{400}{5}=80[/tex]
[tex](0,80)[/tex]
[tex]y=0[/tex]
[tex]20x=400\\\Rightarrow x=\dfrac{400}{20}\\\Rightarrow x=20[/tex]
[tex](20,0)[/tex]
Join the points and the graph representing the situation is obtained.
Learn more:
https://brainly.com/question/14268805
https://brainly.com/question/7744405
Solve the equation -3(x-14)+9x=6x+42. Does the equation have one solution, no solution, or infinitely many solutions?
Answers
Answer:
-3x+42+9x=6x+42
0x=0
x=0
Step-by-step explanation:
there is no solution
Answer:
infinitely many solutions
Step-by-step explanation:
Given
- 3(x - 14) + 9x = 6x + 42 ← distribute and simplify left side
- 3x + 42 + 9x = 6x + 42
6x + 42 = 6x + 42
Since the equation is the same on both sides, then any real value of x is a solution.
That is has infinite solutions
Before a football game can be played, the playing field must be painted. Football fields are rectangles. How can a couch guarantee that the field he is about to paint is a rectangle and not a parallelogram using only a tape measure?
Answers
Answer and Step-by-step explanation:
The only way the coach can guarantee that he is about to paint a rectangle using only a tape measure is by measuring opposite sides of the field and be assured that they are equal.
This is because the opposite sides of a rectangle are always the same, else it is not a rectangle.
Which of the following represents a line parallel to the y-axis
Answers
Answer:
c) x=4
Step-by-step explanation:
HELP PLS IM STRUGGLING .
Math each term with its definition.
a A portion of a line consisting of two points and
e.
Lines that intersect at right angles.
all points between them.
b. A connected straight path. It has no thickness
f. A specific location, it has no dimension and is
represented by a dot.
and it continues forever in both directions.
GA figure formed by two rays with the same
d. A portion ofa line that starts at a point and
The set of all points in a plane that are a foxed
distance from a point caled the center.
&
endpoint.
h. Lines that lie in the same plane and do not
continues forever in one dire ction.
intersect.
Vperpendicular lines
parallel lines
angle
Vcircles
Vline segment
Answers
Answer:
Step-by-step explanation:
Perpendicular angles, E
Line segment, D
Parallel lines, H
Answer:
F - Perpendicular line
C - angle
A -line segment
H - parallel lines
D - circle
G - point
B - line
E - ray
Step-by-step explanation:
If n is any positive 2-digit integer, what is the greatest positive integer that must be a factor of n(n+1)(n+2)(n+3)?
Answers
Step-by-step explanation:
Notice that in n(n + 1)(n + 2)(n + 3):
Exactly 2 of them are multiples of 2,
At least 1 of them is a multiple of 3, and
At least 1 of them is a multiple of 4.
Since one of the multiples of 2 is already counted in the multiple of 4 we can ignore it.
Hence we have 2 * 3 * 4 = 24.
The greater positive integer that must be a factor is 24.
How do you know from a graph if a relationship is a direct variation?
Answers
Answer:
A direct variation is when x and y (or f(x) and x) are directly proportional to each other... For example, if you have a chart that says x and y, and in the x column is 1, 2 and 3, and the y column says 2, 4 and 6... then you know it's proportional because for each x, y increases by 2
Step-by-step explanation:
look at the circumference of each of the circles below. what do you think would be the circumference of a circle with diameter 1 cm?
Answers
Step-by-step explanation:
[tex]circumference \: of \: the \: circle = 2\pi \times \frac{diameter}{2} \\= 2\pi \times radius = 2 \times \pi \times \frac{1}{2} = \pi = 3.14 \: cm[/tex]
Expand the following :
A) 2(x+3)
B) 5(2x-4)
C) 4(2x+1)
D) 6(x-4y)
Answers
Answer:
A. 2x+6 . B. 10x-20 C. 8x+4 D. 6x-24y
Step-by-step explanation:
What is the solution to the inequality 2n+5| > 1?
Answers
Answer:
n < - 3 or n > - 2
Step-by-step explanation:
Inequalities of the type | x | > a , have solutions of the form
x < - a or x > a
Then
2n + 5 < - 1 or 2n + 5 > 1
Solve both inequalities
2n + 5 < - 1 ( subtract 5 from both sides )
2n < - 6 ( divide both sides by 2 )
n < - 3
OR
2n + 5 > 1 ( subtract 5 from both sides )
2n > - 4 ( divide both sides by 2 )
n > - 2
Solution is n < - 3 or n > - 2