Really need some help please.?

Question

Find the points at which y = f(x) = 5x−ln(5x) has a global maximum, a global minimum, and a local, non-global maximum on the interval .1 ≤ x ≤ 3

Answer 1

GLOBAL MINIMUM
f'(x) = 5 - 1/x = 0
x = 0.2
f''(x) = 1/(x^2)
f''(0.2) = 25 > 0
f(0.2) = 1-ln(1) = 1
this means there is a minimum at (0.2, 1)

GLOBAL MAXIMUM
there are no other zeros, so we must check the endpoints. the domain is (0, infinity)
the limit as x approaches 0:
5x goes to 0, so f(x)=-ln(5x)=ln(x^-1)-ln(5), and thus goes to infinity
the limit as x approaches infinity:
f(x)=ln(e^5x/(5x)), this limit goes to infinity
(0, infinity), and (infinity, infinity) are the global maximums

LOCAL MAXIMUM
since there are no relative maximums on this interval, we just need to check the endpoints
f(.1) ~ 1.193
f(3) ~ 12.292
(3, 15-ln(15)) is the local max

Answer 2

global max at 3
global min at .2
max at .1

Answer 3

If your looking for x, the answer is 11.

Answer 4

You really need a graphing tool for this one.

Answer 5

wow thats hard