Question

# Examine the applicability of Mean Value Theorem for the following function.f(x)=[x] for x ϵ [2,2]

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Solution

## Mean Value Theorem holds for a function f:[a,b]→R, if following two conditions holds(i) f is continuous on [a,b](ii) f is differentiable on (a,b)Then, there exists some c∈(a,b) such that f′(c)=f(b)−f(a)b−aMean Value Theorem is not applicable to those functions that do not satisfy any of the two conditions of the hypothesis.Given function f(x)=[x] for x∈[−2,2]Since, the greatest integer function is not continuous at integral points.So, f(x) is not continuous at x={−2,−1,0,1,2} Hence, Mean Value theorem is not applicable to given function.

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