Question #17664

Find the absolute maximum and absolute minimum values of f(x)=x−lnx on the interval [1/8,8].

Expert's answer

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

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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