Answer to Question #17664 in Calculus for hsd

Question

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

Answer 1

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