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
WITCHER [35]
3 years ago
5

Given f(x) = 10 - 16/x, find all c in the interval [2,8] that satisfy the mean value theorem

Mathematics
2 answers:
Katen [24]3 years ago
8 0
F(x)=10-16/x
f'(x)=16/x^2
f'(c)=16/c^2
f(8)=10-16/8=10-2=8
f(2)=10-16/2=10-8=2
f'(c)= \frac{f(b)-f(a)}{b-a} in (2,8),
 \frac{16}{c^2} = \frac{f(8)-f(2)}{8-2} ,
 \frac{16}{c^2} = \frac{8-2}{8-2}

4∈[2,8] is the required point.
Neko [114]3 years ago
3 0

Answer:

c=4

Step-by-step explanation:

By defintion, the mean value theorem is

f'(c)=\frac{f(b)-f(a)}{b-a}

So, in this case, we know that a=2 and b=8.

Now, we need to find f(8) and f(2), by replacing those values into the given function

f(x)=10-\frac{16}{x}\\ f(8)=10-\frac{16}{8}=10-2=8

So, f(b)=f(8)=8.

f(x)=10-\frac{16}{x}\\ f(2)=10-\frac{16}{2}=10-8=2

So, f(2)=2

Then, we replace all values,

f'(c)=\frac{f(b)-f(a)}{b-a}=\frac{8-2}{8-2}=\frac{6}{6}=1

Now, we find the derivative of the function which has to be equal to one,

f(x)=10-\frac{16}{x}=10-16x^{-1}  \\f'(x)=16x^{-2} =\frac{16}{x^{2} } =1

Now, we solve the equation to find the value <em>c, </em>

<em />\frac{16}{x^{2} } =1\\x^{2} =16\\x=4<em />

<em />

<em>Therefore, </em>c=4 is the value inside the given interval that satisfy the mean value theorem.

You might be interested in
Whats the measurement of an angle that cuts off 3/10 of a circle
bija089 [108]
Ahahahahhahahahahhahahahahahhahahahah 6
5 0
3 years ago
1.5k &lt; 6 = ? Help me please.
Naily [24]
K<4 
that should be the answer to your question
3 0
3 years ago
Read 2 more answers
Kendra gets a paycheck of $300 after 5 days of work. At this rate, how much does she get paid for working 24 days?
11Alexandr11 [23.1K]

Answer:

$1440

Step-by-step explanation:

First, find the unit rate by dividing 300 by 5, which equals 60. So, Kendra earns $60 in one day. Then, multiply 60 by 24, which equals 1440. So, Kendra makes $1440 in 24 days. Hope this helped!

7 0
3 years ago
Read 2 more answers
Is 1 a prime or composite number?
mote1985 [20]

Answer:

Hello friends

Step-by-step explanation:

Hope it's helpful

6 0
3 years ago
Read 2 more answers
If you are given the opposite side and hypotenuse, which trig function should you use?
Karo-lina-s [1.5K]

Answer:

sin

Step-by-step explanation:

sin is opp/hyp

7 0
3 years ago
Read 2 more answers
Other questions:
  • Which is the result of 2+2? With negative numbers, fractions, and decimal numbers
    5·2 answers
  • Explain how you can find 3×584 using the expanded form
    13·2 answers
  • How many millimeters are in 50 centimeters?
    10·2 answers
  • Multiple choice. You take a quiz with 6 multiple-choice questions. After you studied, you estimated that you would have about an
    13·1 answer
  • A patient drank 6 ounces of juice,3 cups of water,and half pint of milk.If 1 ounce is equal to 29.6 milliliters,what was the tot
    12·1 answer
  • Suppose a poll is taken that shows that 765 out of 1500 randomly​ selected, independent people believe the rich should pay more
    12·1 answer
  • I got so many points, so i wanna give some away!!
    13·2 answers
  • Help plz , i don't know how to find it
    7·2 answers
  • 2x-8=x+17<br> I need help
    5·2 answers
  • Determine which equation below can be solved to find the value of ∠A.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!