I have already solved both of these questions. Mainly, I just need somebody to check my work and tell me if it's correct. I'd really appreciate it!

Problem 1:Find all local and global minimums and maximums of

in the interval . List the coordinates of each below. If an item doesn't exist, write DNE.

My Answer:First I found the critical points and classified them as local max's or min's.

Second Derivative Test

So f(x) has a local max atand a local min at.

Then I tried to find the global extrema:

So I said that f(x) has a global min of -168 and no global max on this interval

Is all of that correct?

Problem 2:Find the exact global maximum and minimum values of the function

My Answer:

First I tried to find the critical points:

At this point I realized that since there's no interval given, you could have infinitely many critical points with the unit circle, so I decided to graph the function. This is the graph:

After seeing this, I wrote the following as my answer:

There is no global extrama because there is no interval and the graph keeps fluctuating bigger as x approaches negative and positive infinity.

Is that correct? Is that a good way of wording it?

Thank you so much to anybody that replies!