Question

a. Find the critical points of f on the given interval.
b. Determine the absolute extreme values off on the given interval

f(x)= x In(x/5); (0.1,5)

Answer 1

f = x ln(x/5)
f' = 1 + ln(x/5)
critical points where f'=0, so
1 + ln(x/5) = 0
x = 5/e

f(5/e) = -5/e
now, checking the endpoints of the interval
f(1/10) = -ln(50)/10
f(5) = 0

So, looks like the min is -5/e, max is 0.