For the function f(x) = x + 1/x, x ∈ [1, 3], the value of c for mean value theorem is ______.

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For the function f(x) = x + 1/x, x ∈ [1, 3], the value of c for mean value theorem is sqrt(3). Explanation: Given that: f(x) = x + 1/x, x ∈ [1, 3] We know that if f(x) = x + 1/x, x ∈ [1, 3] satisfies all the conditions of mean value theorem then f'(c) = `("f"("b") - "f"("a"))/("b" - "a") where a = 1 and b = 3 $\Rightarrow$ 1 - 1/"c"^2 = ((3 + $\frac{1}{3}$) - (1 + $\frac{1}{1}$))/(3 - 1) $\Rightarrow$ 1 - 1/"c"^2 = ($\frac{10}{3}$ - 2)/2 $\Rightarrow$ 1 - 1/"c"^2 = $\frac{4}{6}$ = $\frac{2}{3}$ $\Rightarrow$ - 1/"c"^2 = $\frac{2}{3}$ - 1 $\Rightarrow$ - 1/"c"^2 = -$\frac{1}{3}$ $\Rightarrow$ 1/"c"^2 = $\frac{1}{3}$ $\Rightarrow$ c = +- sqrt(3). Here c = sqrt(3) ∈ (1, 3)`.

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