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Question

The value of c prescribed by Lagrange's mean value theorem, when f(x)=x24,a=2 and b=3, is

A
2.5
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B
5
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C
3
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D
3+1
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Solution

The correct option is B 5
Clearly, f(x)=x24 is continuous on [2, 3] and differentiable on (2, 3).
So, by Lagrange's mean value theorem, there exists c ε(2, 3) such that
f(c)=f(3)f(2)32
cc24=50
[f(x)=x24f(x)=xx24]
c2=5(c24)
4c2=20
c=5

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