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Question

Examine the applicable of MVT for all three functions.

f(x)=1x2 for xϵ[1, 2]

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Solution

Here, f(x)=1x2, which is a polynomial function.

Since, a polynomial function is continuous and derivable at all xϵR, therefore

(a) f is continuous in [1, 2]

(b) f is derivable in (1, 2) f satisfies conditions of MVT in [1, 2]

Hence, there exists atleast one real cϵ[1, 2] such that

f(c)=f(2)f(1)21 ( f(c)=f(b)f(a)ba) 2c=(122)(112)21 ( f(x)=1x2, f(x)=2x) 2c=3 c=32 ϵ (1, 2) MVT is verified for the given function in the given interval.


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