Question

State why the Mean Value Theorem does not apply to the function f(x) = (2) / (x+1)^2

Answer 1

I dont know much about the mean value theorem
Besides that f'(c) = f(b) - f(a) over b-a

Answer 2

hint: look at the second sentence on this link

http://www.sosmath.com/calculus/diff/der11/der11.html

Answer 3

btw you didn't state an interval

Answer 4

Ok so
Theres an interval [a,b]
And c is somewhere in the middle
When [a,b] is continuous and (a,b) is differentiable

Answer 5

yes those are the conditions needed to be satisfied for the MVT to work

if f(x) is undefined anywhere on [a,b] then it won't work. In this case, it's undefined when x = -1. However your teacher didn't state an interval. I guess s/he just means in general?

Answer 6

Oh im sorry
The interval is [-3,0]

Answer 7

ok that makes things easier. So because x = -1 is in that interval, the MVT won't work

x = -1 causes a division by zero error

Answer 8

if you adjust the interval to not have -1 in it, say [10,20], then the MVT would work

Answer 9

Ok thanks
I have a question
Say it was continuous
How to prove it is differentiable on (-3,0)?

Answer 10

find the derivative function and prove it's continuous

Answer 11

`f(x) is differentiable` is the same as saying `f ' (x) is continuous`

Answer 12

Oh ok. Thanks a lot.

Answer 13

you're welcome