Examine the applicability of Mean Value Theorem for all three functions given below
(i) `f(x)=[x], " " x in [5,9]`
(ii) `f(x)=[x], " " x in [-2,2]`
(iii) `f(x)=1-x^(2), " " x in [1,2]`

Explanation

To examine the applicability of the Mean Value Theorem (MVT) for the given functions, we need to check two conditions for each function:

1. The function must be continuous on the closed interval \([a, b]\).
2. The function must be differentiable on the open interval \((a, b)\).

Let's analyze each function step by step.

### Part (i): \( f(x) = [x] \) for \( x \in [5, 9] \)
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