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Question

If from Lagrange's Mean Value Theorem, we have f'(x1)=f(b)f(a)ba, then .

A
a<x1b
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B
ax1<b
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C
ax1b
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D
a<x1<b
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Solution

The correct option is D a<x1<b
According to the Lagrange's Mean Value Theorem, if f(x) is defined on [a, b] such that
(i) it is continuous on [a, b]
(ii) it is differentiable on (a, b)
Then, there exists a real number x1(a, b) such that f'(x1)=f(b)f(a)ba.

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