Question

Find c using the Mean Value Theorem.

Answer 1

Decide whether the function f=1+1/x satisfies the hypotheses of the MVP on the interval [a,b]=[1,4].

Answer 2

So f(4)=5/4 and f(1)=2
((5/4)-2)/(4-1) = -9/4

Answer 3

\[\ln (x)=\frac{ -9 }{ 4 }\]

Answer 4

c=\[e ^{-9/4}\] I thought that would be the right answer but it wasn't.

Answer 5

-9/4 should be -1/4

Answer 6

why did you integrate 1/x and differentiate 1?

Answer 7

How did I integrate?

Answer 8

d/dx (x^-1) is not ln(x)

Answer 9

you can use power rule to differentiate 1/x aka x^(-1)

Answer 10

also I think your arithmetic was a little off when finding the average velocity of f on [a,b]

Answer 11

Thanks guys. I guess I got them mixed up.

Answer 12

on [1,4]

Answer 13

\[\frac{\frac{5}{4}-2}{4-1} =\frac{5-8}{16-4}=?\]
multiply top and bottom by 4 to make a bit easier on you

Answer 14

-1/4 whoops...

Answer 15

so you should have the equation
\[(1+\frac{1}{x})'=\frac{-1}{4} \\ \text{ where } (1+\frac{1}{x})' \neq \ln(x) \text{ of course }\]

Answer 16

So, -1/x^2=-1/4

Answer 17

right or x^2=4

just remember you are looking for x in the interval [1,4]

Answer 18

or it really should be the interval (1,4)

Answer 19

I got it. Thanks for the help @freckles! I was just making some simple mistakes.

Answer 20

np
:)
have a nice day

Answer 21

@ 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?