find all values of c in the open interval (a, b) such that f'(c)=(f(b)-f(a))/(b-a)
f(x)=√(4-x), [-5,4]
![Find All Values Of C In The Open Interval (a, B) Such That F'(c)=(f(b)-f(a))/(b-a)f(x)=(4-x), [-5,4]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/yMklNJtdn9H9OGFOYxpw7zoJAv6M7I7D.jpeg)
Answers
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Work Shown:
Compute the function value at the endpoints
[tex]f(x) = \sqrt{4-x}\\\\f(-5) = \sqrt{4-(-5)} = 3\\\\f(4) = \sqrt{4-4} = 0\\\\[/tex]
With a = -5 and b = 4, we have
[tex]f'(c) = \frac{f(b)-f(a)}{b-a}\\\\f'(c) = \frac{f(4)-f(-5)}{4-(-5)}\\\\f'(c) = \frac{0-3}{9}\\\\f'(c) = -\frac{1}{3}\\\\[/tex]
So,
[tex]f(x) = \sqrt{4-x}\\\\f'(x) = -\frac{1}{2\sqrt{4-x}}\\\\f'(c) = -\frac{1}{3}\\\\-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\[/tex]
Use algebra to solve for c
[tex]-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\\frac{1}{2\sqrt{4-c}} = \frac{1}{3}\\\\3 = 2\sqrt{4-c}\\\\2\sqrt{4-c} = 3\\\\\sqrt{4-c} = \frac{3}{2}\\\\4-c = \frac{9}{4}\\\\c = 4-\frac{9}{4}\\\\c = \frac{16-9}{4}\\\\c = \frac{7}{4}\\\\[/tex]
Related Questions
Someone help me please
Answers
Answer:
x = 6.3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tan∅ = opposite over adjacentStep-by-step explanation:
Step 1: Define
We have a right triangle triangle. We can use trig to find the missing length.
Step 2: Identify Variables
POV from the angle measure
Angle = 64°
Opposite = 13
Adjacent = x
Step 3: Solve for x
Substitute: tan64° = 13/xMultiply x on both sides: xtan64° = 13Isolate x: x = 13/tan64°Evaluate: x = 6.34052. A electric jug was sold allowing 20% discount
with Profit of Rs.120. If the jug was sold
allowing 30% discount, there would have
been loss of Rs. 270. Find the MP of the jug.
solu
Answers
9514 1404 393
Answer:
marked price = Rs. 3900
Step-by-step explanation:
The difference between the discounts is 30% -20% = 10% of the marked price. The difference in Rs is 120 -(-270) = 390. If Rs. 390 is 10% of the marked price, then the marked price is (Rs. 390)/(0.10) = Rs. 3900.
The marked price is Rs. 3900.
_____
Check
A 20% discount from 3900 is a price of 3120. If the profit is 120, the cost price is 3000. A 30% discount from 3900 is 2730. This is 270 below the 3000 cost price, so our answer is consistent with problem requirements.
2(x -1) + 1/2 (4x + 6)=5
Answers
X: -4. Y: -3
Step-by-step explanation:
How would I translate 2=x-9 into a verbal sentence?
Answers
Answer:
Two equals X minus Nine
4x-5=x-1+3x I need help
Answers
Answer:
x = no solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define equation
4x - 5 = x - 1 + 3x
Step 2: Solve for x
Combine like terms: 4x - 5 = 4x - 1Subtract 4x on both sides: -5 ≠ -1Here we see that -5 does not equal -1.
∴ This equation has no solutions.
Answer each question and explain your reasoning. How long is 50% of 60 minutes?
Answers
Answer: 6mins
Step-by-step explanation:
6mins, because 10x6= 60 (or) 60/10=6
Answer:
30 minutes
Step-by-step explanation:
60 divided by 2 which would give you 30 minutes.
PLEASE ANSWERR CORRECTLY!!!!!!!!
WILL MARK BRAINLIEST FOR CORRECT ANSWER!!!!!!!!
At the beginning of the week, Naveen has 87 trading cards. On Monday, he gets 9 more. On Tuesday, he gives 16 away. On Wednesday, he is given 3 by a friend. On Thursday, he sells all of his cards to a collector. The collector pays him a rate of c for every card that Naveen has. If Naveen earns $124.50 from the sale, what is c, the rate that the collector pays for each card?
A) $1.08
B) $1.50
C) $41.50
D) $83.00
PLEASE ANSWER CORRECTLY!!!!!!!!
HURRY!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
B) $1..50
Step-by-step explanation:
First, how many trading cards did Naveen have?
87 + 9 - 16 + 3 = 83
$124.50 / 83 = $1.50
._. kan someone help?
Answers
Answer:
The third one
Step-by-step explanation:
it number 3 one no prob
Step-by-step explanation:
.
Solve for x
5x – 7 = 19
Give your answer as an

Answers
5x - 7 = 19
Add 7 to both sides:
5x = 26
Divide both sides by 5:
x = 26/5
[tex]5x - 7 = 19[/tex]
Move -7 to another side and become + 7. Whenever we move to another side, we change the sign/operator to opposite. Ergo, changing from plus to minus and multiply to divide.
[tex]5x = 19 + 7 \\ 5x = 26[/tex]
We are at this part. Now to move 5 which is multiplying the x. So we move 5 from multiply to divide 26.
[tex]x = \frac{26}{5} [/tex]
Ergo, the answer is x = 26/5
Find the intercept of the y axis for 6x + 4y – 12z = 36. will give brainlest
(6, 4,-12)
(0, 0, -3)
(6, 0, 0)
(0, 9, 0)
Answers
Answer: ( 0, 9, 0)
Step-by-step explanation: They both equal 36 but i think (0, 9, 0) is the better fit out of (0, 9, 0), and (6, 0, 0)
Hope this helps :)
ection 1
If Frances can paint of a wall in 20 minutes, how long will it take her to paint a room with 4 walls?
60 minutes
100 minutes
400 minutes
500 minutes
Answers
PLEASE HELP MEEEEE!!!!!
Answers
Answer:
I think it might be d
Step-by-step explanation:
A recipe requires 1 2/3 cups of sugar. If Mrs.Marina is going to make one and one half of the recipe, then how much sugar does she need
Answers
5/3 + 5/6
10/6 + 5/6
she needs 15/6 or 2 3/6 or 2 1/2 cups of sugar
Mrs. Marina requires 5/2 or 2.5 cups of sugar to make one and one half of the recipe.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
A recipe requires 1 (2/3) cups of sugar.
That is 1 recipe requires = 1(2/3) cups of sugars
= 5/3 cups of sugar
Now, Marina is going to make one and one half of the recipe and to find the sugar he needed we simply multiply 1(1/2) both the sides :
1 recipe requires = 5/3 cups of sugar
1(1/2) recipe requires = (5/3) x 1(1/2) cups of sugar
3/2 recipe requires = (5/3) x (3/2) cups of sugar
3/2 recipe requires = 5/2 cups of sugar or 2.5 cups of sugar.
Therefore, Mrs. Marina requires 5/2 or 2.5 cups of sugar to make one and one half of the recipe.
Read more about ratio at:
https://brainly.com/question/17869111
#SPJ5
What is the volume of this pyramid???????
Answers
Answer:
Step-by-step explanation:
A of base: l ×w =5×4=20cmsquared
Missing length of c=a+b=c
C=6+2
C=8cm
A of side 1= b×h÷2 ×2
= 5×8÷2×2
= 40 ÷2×2
=20 ×2
= 40 cm squared
A of side 2= b×h÷2×2
= 4×8÷2×2
= 32 ÷ 2 ×2
= 16 ×2
= 32cm squared
Total of pyramid is = area of base + A
off side 1 + A if side 2
=92 cm cubed
what would be the best first step to solve this
(4x-9x)(12+8x)=9(4x)
Answers
Answer:
open the brackets is the first step
Step-by-step explanation:
4x(12 + 8x) -9x( 12+8x) = 36x
48x + 32x^2 -108x -72x^2 =36x
32x^2 - 72^2 + 48x - 36x - 108x = 0
-40x^2 -96x = 0
find x using quadratic formular
PLEASE PLEASE HELP!!! urgently
f(x)=-2x+3
g(x)=3x+3
find f(1-x) + g(1-x)
Answers
Answer:
-5x + 11
Step-by-step explanation:
All you're doing is substituting.
f(x)=-2x+3
f(1-x) = 2(1-x)+3
= 2 - 2x +3
= -2x + 5
g(x)=3x+3
g(1-x) = 3(1-x)+3
= 3 - 3x + 3
= -3x + 6
Now add them together and combine like terms:
f(1-x) + g(1-x)
-2x + 5 + -3x + 6
= -5x + 11
Fill in the table using this function rule
Answers
What is the constant in this situation?
Answers
Why? It says “purchased at a constant price p”
Hope this helps :D
What is the common difference or ratio?
A. The common difference is 0.38.
B.
The common difference is 0.76.
C. The common ratio is 0.99.
D. The common ratio is 1.02.
Answers
Answer:
The correct answer is A. The common difference is 0.38
Step-by-step explanation:
Hope i helped! Have a great day <3
The ratio of boys to girl in a school is 5:7 if there are 600 students, how many girls are there
Answers
Answer:
350 girls
Step-by-step explanation:
So,
The secret to solving problems with ratios is to find the value of one unit.
5:7 = 12 units total
To find one unit, divide the total number of students by the total number of units.
600/12 = a
Simplify
50/1 = a
50 = a
The value of each unit is 50.
Now, multiply the units by the numbers in the ratio.
50(5) = b
250 = boys
50(7) = x
350 = x
There are 350 girls.
Is the last option correct?
Answers
Answer:
yes it is
Step-by-step explanation:
If triangle ABC is similar to triangle DEF, what is the value of x?
12 cm
36 cm
15 cm
5 cm
Answers
Answer:
x = 15 cmStep-by-step explanation:
If triangle ABC is similar to triangle DEF, then:
[tex]\dfrac{AC}{DF}=\dfrac{BC}{EF}[/tex]
Therefore:
[tex]\dfrac{x}{5}=\dfrac{12}{4}\\\\\dfrac{x}{5}=3\\\\x=15[/tex]
In Science class, 23 out of 25 students are present. What percent of the class is present?
Answers
Answer:
94.25% of the class is present
i hate school okokokokokok
Answers
Answer:
Thanks for the free points...
I love school by the way
Answer:
hey
can you give me a brainliest
Step-by-step explanation:
worth a lot of points! please help and explain your answer tysm
Answers
Answer:
option c is incorrect
because the value of tan B will be perpendicular/base
so tan B=5/12.
mark me brainlist
Please help me out :(
Answers
Answer:
True
True
False
Step-by-step explanation:
Rate of Change is slope. There is no change in slope as the line is straight.
Using the slope formula:
[tex]m=\frac{x_{2}-x_{1} }{y_{2}-y_{1}} \\m=\frac{4-0}{1-0}\\m=4[/tex]
Where m is slope
Since gold beads are on the x-axis, that means there are 4 black beads per gold bead
Gabriel is buying bagels for a family gathering. Each bagel costs $1.75. Answer the questions below regarding the relationship between the total cost and the number of bagels purchased.
The independent variable, x, represents the
, and the dependent variable is the
, because the
depends on the
.
A function relating these variables is N(x) =N(x)=
.
So N(14) =N(14)=
, meaning 1414
.
Answers
Answer:
Independent Variable: Number of bagels bought
Dependent Variable: Total cost because it depends on the number of bagels bought.
Function: N(x)=1.75x
So, if x is the number of bagels bought, N(14) means that 14 bagels were bought. So you multiply 14 by the price; 1.75. So, N(x)=1.75*14 = $24.5
Step-by-step explanation:
Answer:
The independent variable, x, represents the number of bagels purchased, and the dependent variable is the total cost of the bagels, because the total cost of the bagels depends on the number of bagels purchased.
A function relating these variables is V(x) =1.75x.
So V(14) = 24.5, meaning 14 bagels will cost 24.5 dollars.
Step-by-step explanation:
Have a good day :)
Please give me Thanks
Who here is in 8th grade?
Answers
Answer: I am in 8th grade but am in virtual
pls help. polynomials solving equations
Answers
Answer:
+9or -9 is the answer ☺️ you
Answer:
y will be equal to 0, 9, or 1
(y=0, 9, 1)
what is the rate of change ??
Answers
Answer:
4/1 or 4
Step-by-step explanation:
it goes 4 on the y axis after 1 on the x axis