#### Question

Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2.

#### Solution

Mean Value Theorem states that for a function f:[a,b] -> R, if

(a) *f* is continuous on [*a*, *b*]

(b) *f* is differentiable on (*a*, *b*)

ii) f (x) = [x] for x ∈ [– 2, 2]

It is evident that the given function *f* (*x*) is not continuous at every integral point.

In particular, *f*(*x*) is not continuous at *x *= −2 and *x *= 2

⇒ *f* (*x*) is not continuous in [−2, 2].

The differentiability of *f* in (−2, 2) is checked as follows.

Let *n *be an integer such that *n* ∈ (−2, 2).

Is there an error in this question or solution?

Solution Examine the Applicability of Mean Value Theorem for All Three Functions Given in the Above Exercise 2. Concept: Mean Value Theorem.