local max & min

Question

for f(x) = x - lnx, and 0.1 ≤ x ≤ 2, find the following

a) find the values of x for which f(x) has a local maximum ( in increasing order)

x =

x =

b) find the value of x for which f(x) has a global maximum.

x =

Answer 1

Set the f'(x)=0 and solve for x....the result is x=1 and graphically this is a local minimum.

The absolute max occurs at the left end point.