Misc 2 - Show that f(x) = log x/x has maximum at x = e - Local maxima and minima

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  1. Chapter 6 Class 12 Application of Derivatives
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Misc 2 Show that the function given by f(x) = log has maximum at x = e. Let f = log Step 1: Finding f f = f = log f = log . . log 2 f = 1 2 log 2 f = 1 log 2 Step 2: Putting f = 0 1 log 2 =0 1 log = 0 log = 1 = e Step 3: Finding f f = 1 log 2 Diff w.r.t. f = 1 log 2 f = 1 log . 2 2 . 1 log 2 2 = 0 1 . 2 2 1 log 4 = 1 2 2 1 log 4 = 2 1 log 4 = 1 + 2 1 log 4 = 1 + 2 2 log 4 = 3 2 log 4 f = 3 2 log 3 Putting = e f = 3 2 log 3 = 3 2 3 = 1 3 = 1 3 < 0 f < 0 at = e . = e is point of maxima f is maximum at = e.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.