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!
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.
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 at and 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?
Find the exact global maximum and minimum values of the function
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!