If f(x) = tan(x), does the Mean Value Theorem apply on the interval [0, 2] and why?
The Mean Value Theorem does not apply because f(x) is not continuous on the closed interval [0, pi].
The Mean Value Theorem applies because f(x) is continuous on [0, pi].
The Mean Value Theorem applies because, f(x) is differentiable on the closed interval [0, pi].
The Mean Value Theorem applies because f(x) is differentiable on the open interval (0, pi).

Question

If f(x) = tan(x), does the Mean Value Theorem apply on the interval [0, 2] and why? 
       The Mean Value Theorem does not apply because f(x) is not continuous on the closed interval [0, pi].
        The Mean Value Theorem applies because f(x) is continuous on [0, pi].
        The Mean Value Theorem applies because, f(x) is differentiable on the closed interval [0, pi].
        The Mean Value Theorem applies because f(x) is differentiable on the open interval (0, pi).

phi · Answer

This is similar to your other question

To use the Mean Value Thm you need
a function that satisfies both of the following:
it is continuous on the closed interval [a,b].
 it is differentiable on the open interval (a,b).

If you have a nice curve from tan(0) to tan(2)  (assume these numbers are radians)
then you are good to go.

You should know that tan(pi/2) approaches infinity...  (not continuous)
what value is pi/2 ?  about 3.14/2  or 1.57 radians

do you see a problem?  0....1.57*.....2

* trouble!