Find the absolute maximum and absolute minimum values of f(x)=x−lnx on the interval [1/8,8].
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Expert's answer
2012-11-06T12:08:35-0500
f(x) is continuous so we need to check only ends of theinterval and points where f'=0 f'=1-1/x f'=0 so x=1 f(1/8)=1/8-ln(1/8)=1/8+ln(8) f(1)=1 f(8)=8-ln(8) the greatest value is at x=8 f=8-ln(8) the smallest value is at x=1 f=1
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