Find the interval on which the function x/logx is increasing or decreasing.

Question

SHAIK AASIF AHAMED · Answer

f ( x )= x/ log x f '( x )=log x −1/(log x )2 N ow the function is increa sin g or decrea sin g in a particular intervals depends upon the sign of derivatives . T he function is increa sin g in the interval where the derivative is positive and decrea sin g in the intervals where the derivative is negative . H ence for increa sin g in a particular interval f '( x )>0 ⇒log x −1(log x )2>0 ⇒log x >1 ⇒ x > e And for decrea sin g in a particular interval , f '( x )<0 ⇒log x −1(log x )2<0 ⇒log x <1 ⇒ x < e but the domain of f ( x ) is x >0 H ence f ( x ) is increa sin g in ( e ,∞) and decrea sin g in (0, e ) and at x = e there is a minima Thanks & Regards Shaik Aasif Ahamed askIITians Faculty

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Find the interval on which the function x/logx is increasing or decreasing.

Find the interval on which the function x/logx is increasing or decreasing.

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Find the interval on which the function x/logx is increasing or decreasing.

Find the interval on which the function x/logx is increasing or decreasing.

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