1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gavmur [86]
3 years ago
10

Find all values of c in the open interval (a, b) such that f'(c)=(f(b)-f(a))/(b-a)

Mathematics
1 answer:
timama [110]3 years ago
6 0
<h3>Answer:   c = 7/4</h3>

================================================

Work Shown:

Compute the function value at the endpoints

f(x) = \sqrt{4-x}\\\\f(-5) = \sqrt{4-(-5)} = 3\\\\f(4) = \sqrt{4-4} = 0\\\\

With a = -5 and b = 4, we have

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}\\\\

So,

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}\\\\

Use algebra to solve for c

-\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}\\\\

You might be interested in
The temperature overnight in Sitka, Alaska was 12 below zero. How should this be written?
Bingel [31]

Answer:

-12°

Step-by-step explanation:

it is negative because it it below zero.

6 0
2 years ago
Edith ordered 588 tomatoes for the produce section. if there are 84 per crate, how many crates will she receive?
Igoryamba

Answer:

7 crates of tomatoes

Step-by-step explanation:

588÷84=7

3 0
3 years ago
Read 2 more answers
Last year the cost of Mr. patten’s car insurance was 86.80 per month. This year it inscreased by 5 percent. What was the cost of
marissa [1.9K]

Answer:4.34

Step-by-step explanation:

3 0
3 years ago
I NEED HELP ASAP! In a magic square, the sum of the numbers in each row, column, and diagonal is the same. Write and solve equat
Trava [24]

Answer:

a=22,\\b=31,\\c=13

Step-by-step explanation:

When choosing equations to write, make sure you choose a pair that allow you to isolate a variable and solve for it.

Sample solution:

a+25+28=16+25+34,\\\\a+28=16+34,\\a+28=50,\\a=\boxed{22}

16+b+28=16+25+34,\\b+44=75,\\b=\boxed{31}

34+c+28=16+25+34,\\c+28=41,\\c=\boxed{13}

8 0
2 years ago
3x+6=30 i need some help
goldenfox [79]

Answer:

24

Step-by-step explanation:

3x+6=30

Get the co-efficient by itself

3x +6=30

     -6.   -6

3x=24

Divide by 3 on both sides

24/3

x =8

4 0
3 years ago
Read 2 more answers
Other questions:
  • Write or draw to explain two ways you can find the sum of 3+4+5
    7·2 answers
  • What is greater 4 meters or 450 centimeters
    6·1 answer
  • What is the midpoint of the segment shown below ?
    10·2 answers
  • The mean of 4 test scores is 90. What is the sum of the scores?
    8·2 answers
  • Ed is 7 years older than Ted.Ed's age is also 3/2 times Ted's age.How old is Ed and Ted
    5·2 answers
  • You paid $700 for a new guitar. Your guitar cost $20 less than twice the cost of your friend's guitar.
    15·2 answers
  • For the linear equation, find the product of 8 and the linear equation, and solve both equations for y.
    13·1 answer
  • Factor completely 9-25x^2=
    8·2 answers
  • (x+4)+(x-3)+(2x+2)+(x^2+3x+1)
    9·1 answer
  • I am really overwhelmed with this new topic in mathematics, I wondered if you could help me understand it? It's fine if you don'
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!