find maxima and minima of y=log x/x
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y = logx/x
dy/dx = ( x×1/x -logx )/x² = ( 1 - logx)/x²
dy/dx > 0
when , ( 1 -logx ) > 0 and x² > 0 x € R
logx < 1
x < e
when ,
dy/dx < 0 then,
( 1 -logx) < 0
logx > 1
x >e
hence ,
x< e function is increasing
and x>e , function is decreasing
so, at x = e function gain maximum value
so, maximum value = loge/e = 1/e
minima doesn't possible
dy/dx = ( x×1/x -logx )/x² = ( 1 - logx)/x²
dy/dx > 0
when , ( 1 -logx ) > 0 and x² > 0 x € R
logx < 1
x < e
when ,
dy/dx < 0 then,
( 1 -logx) < 0
logx > 1
x >e
hence ,
x< e function is increasing
and x>e , function is decreasing
so, at x = e function gain maximum value
so, maximum value = loge/e = 1/e
minima doesn't possible
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