In which interval is the function f(x) = frac | vedclass

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(B) Given the function $f(x) = \frac{x}{\ln x}$.To find the interval where the function is increasing,we calculate the derivative $f'(x)$:$f'(x) = \fr

Vedclass · Accepted Answer

$(e, \infty)$

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(B) Given the function $f(x) = \frac{x}{\ln x}$.To find the interval where the function is increasing,we calculate the derivative $f'(x)$:$f'(x) = \frac{(\ln x)(1) - x(\frac{1}{x})}{(\ln x)^2} = \frac{\ln x - 1}{(\ln x)^2}$.For the function to be increasing,we must have $f'(x) > 0$.Since $(\ln x)^2 > 0$ for all $x$ in the domain (where $x > 0$ and $x 
eq 1$),the condition $f'(x) > 0$ implies:$\ln x - 1 > 0$$\ln x > 1$$x > e$.Thus,the function is increasing in the interval $(e, \infty)$.

In which interval is the function $f(x) = \frac{x}{\ln x}$ increasing?

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