UnknownRandom
  • UnknownRandom
Find c using the Mean Value Theorem.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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UnknownRandom
  • UnknownRandom
Decide whether the function f=1+1/x satisfies the hypotheses of the MVP on the interval [a,b]=[1,4].
UnknownRandom
  • UnknownRandom
So f(4)=5/4 and f(1)=2 ((5/4)-2)/(4-1) = -9/4
UnknownRandom
  • UnknownRandom
\[\ln (x)=\frac{ -9 }{ 4 }\]

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UnknownRandom
  • UnknownRandom
c=\[e ^{-9/4}\] I thought that would be the right answer but it wasn't.
UnknownRandom
  • UnknownRandom
-9/4 should be -1/4
freckles
  • freckles
why did you integrate 1/x and differentiate 1?
UnknownRandom
  • UnknownRandom
How did I integrate?
phi
  • phi
d/dx (x^-1) is not ln(x)
freckles
  • freckles
you can use power rule to differentiate 1/x aka x^(-1)
freckles
  • freckles
also I think your arithmetic was a little off when finding the average velocity of f on [a,b]
UnknownRandom
  • UnknownRandom
Thanks guys. I guess I got them mixed up.
freckles
  • freckles
on [1,4]
freckles
  • freckles
\[\frac{\frac{5}{4}-2}{4-1} =\frac{5-8}{16-4}=?\] multiply top and bottom by 4 to make a bit easier on you
UnknownRandom
  • UnknownRandom
-1/4 whoops...
freckles
  • freckles
so you should have the equation \[(1+\frac{1}{x})'=\frac{-1}{4} \\ \text{ where } (1+\frac{1}{x})' \neq \ln(x) \text{ of course }\]
UnknownRandom
  • UnknownRandom
So, -1/x^2=-1/4
freckles
  • freckles
right or x^2=4 just remember you are looking for x in the interval [1,4]
freckles
  • freckles
or it really should be the interval (1,4)
UnknownRandom
  • UnknownRandom
I got it. Thanks for the help @freckles! I was just making some simple mistakes.
freckles
  • freckles
np :) have a nice day
UnknownRandom
  • UnknownRandom
@ freckles Can you help me solve this one when you get a chance? Farmer Alex has 32 llamas each of whom needs 1000000 square feet of grazing area. He wants to enclose a rectangular pen along a straight river, where he does not need fence. What is the minimum amount of fencing he must use to build his pen?
UnknownRandom
  • UnknownRandom
|dw:1449182663206:dw|
UnknownRandom
  • UnknownRandom
|dw:1449182746673:dw|
phi
  • phi
perimeter is x+2y area is xy= 32e6 so y= 32e6/x and p(x)= x + 64e6*x^(-1) take the derivative and set equal to 0
UnknownRandom
  • UnknownRandom
@phi I did all of that and got 8000. Are there more steps after that?
phi
  • phi
you found the width x the question asks for What is the minimum amount of fencing he must use to build his pen? so you need the corresponding length x+2y x is 8000 y = 32e6/8e3 = 4e3 and the perimeter is 8e3+ 2*4e3= 8e3+8e3= 16e3 i.e. 16,000 ft
UnknownRandom
  • UnknownRandom
That makes sense.
UnknownRandom
  • UnknownRandom
I didn't know you had to take the derivative of the perimeter.
UnknownRandom
  • UnknownRandom
It makes sense now though once I put two and two together.

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