Question

Hi all! I have a question left on my problem set and I'd like to check my answer :)

"verify that the function satisfies the hypotheses of the mean value theorem on the given interval. Then find all numbers c that satisfy the conclusion of the mean value theorem f(x) = 1/x [1,3]"

Answer 1

So, I have the derivative as f'(x)= -1/(x^2)

Answer 2

The value c I got is sqrt(3/4)

Answer 3

I'm a bit confused about this problem :)

Answer 4

:/

Answer 5

f(1)=1/1=1
f(3)=1/3
The average slope between these two points
\[\frac{ \frac{ 1 }{ 3 } -1 }{ 3-1 }= -\frac{ 1 }{ 3 }\]

Answer 6

f'(x)= -1/(x^2) as you stated before
make it equal to -1/3
-1/(x^2)=-1/3
\[x=\pm {\sqrt{3}}\]

Answer 7

The solution is only the + as the - lies outside the interval [1,3]

Answer 8

If you need further info check this video:
http://www.youtube.com/watch?v=xYOrYLq3fE0