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Question

For the function f(x)=x+1x, x(1, 3], the value of c for which the Lagrange's Mean Value Theorem holds is .

A
1
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B
3
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C
2
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D
2
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Solution

The correct option is B 3
Since, the Lagrange's Mean Value Theorem holds for the given function f(x)=x+1x, x(1, 3]. Therefore, there exists a value c in [1, 3] such that f'(c)=f(b)f(a)baf'(c)=f(3)f(1)3111c2=3+13(1+1)2 (f'(x)=11x2]11c2=432=231c2=13c=3.

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