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
1: n/-3 - 8 &lt; 17<br> 2: n/-2 + 11 &gt; 17
cupoosta [38]

Answer:

1: n > -75

2: n < -12

Step-by-step explanation:

1: n/-3 - 8 < 17

n/-3 (- 8 + 8) < 17 + 8

n/-3 < 25

n/-3(-3) < 25(-3)

n < -75

n > -75 (switch symbol when you divide or multiply by a negative number)

2: n/-2 + 11 > 17

n/-2 (+ 11 - 11) > 17 - 11

n/-2 > 6

n/-2(-2) > 6(-2)

n > -12

n < -12 (switch symbol when you divide or multiply by a negative number)

7 0
3 years ago
Variance is_________.
katrin [286]

Answer:

B

Step-by-step explanation:

Variance can be said to be a measure of dispersion for a random sample.

Variance = pq/n

When given the variance, we can find the standard deviation.

Standard deviation = √variance

= √pq/n

3 0
3 years ago
Walter pays $2.53 to ship a package
Ivan

Answer:

what is the rest of the equation?

Step-by-step explanation:

7 0
3 years ago
-6+8x=-38<br> What is the answer and explain how you got it step by step
Anarel [89]
-6 +8x = -38
8x = -32
x = -4
I did this by first adding 6 to both sides to get 8x by itself. I then divided by 8 to get x by itself. I remembered to use the - - + rule (Two negatives make a positive, a positive and a negative make a negative). Hope this helps!
3 0
3 years ago
Read 2 more answers
The perimeter of a rectangle is 46 in and the diagonal is 17 in. Find the area of the rectangle.
OlgaM077 [116]
P=2*(L+l)=46
L+l=46:2
L+l=23
(L+l)^2=529
(L^2+l^2)+2l*L=529

D= V L^2+l^2= 17
L^2+l^2=289

so 289+2l*L=529
     2l*L=529-289=240
l*L=240:2
A=120 


5 0
3 years ago
Other questions:
  • After completing the following frequency table, find the mode?
    10·1 answer
  • What is the order of rotational symmetry for the figure?
    12·1 answer
  • If a Play Station was bought for $450 after a 10% discount what was the original price of the Play Station?
    11·1 answer
  • Name a slave state which chose to stay in the union and didn’t join the confederacy? *URGENT*
    14·1 answer
  • -4(-11+4n) -3( -2n+9)
    12·2 answers
  • All of the following are equivalent except _____.<br> 4 · y<br> 4 + y<br> 4y<br> (4)(y)
    10·2 answers
  • Find the shaded area
    15·1 answer
  • If you roll a cube 30 times how many 3s​
    14·1 answer
  • BRAINLIEST TO WHOEVER ANSWERS CORRECLTY
    9·2 answers
  • Find the value of w (u(2))
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!