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in Continuity and Differentiability by (28.7k points)
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For the function f(x) = x + \(\frac{1}{\text{x}},\) x ∈[1, 3], the value of c for the Lagrange’s mean value theorem is

A. 1

B. \(\sqrt{3}\)

C. 2

D. None of these

1 Answer

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by (29.1k points)
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Best answer

Correct answer is B.

It shows that f(x) is continuous on 1, 3 and derivable on 1, 3.

So, both the conditions of Lagrange’s Theorem are satisfied.

Consequently, there exists c Є 1, 3 such that

x = \(\pm \sqrt{3}\) Hence, c = \(\sqrt{3}\) Є (1, 3) such that f'(c) = \(\frac{f(3) - f(1)}{3 - 1}.\)

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