Hi everyone. I have a question on one of my homework problems.

Q. Find the local max./min. values and the saddle point(s) of the function

So I started doing this problem and it was looking really messy so I went on cramster and got this:

Step 1

Step 2

There's already a mistake here since you forgot to differentiate the second summand above. It should be:

, and this

alone already tells you that all the points on the unit circle around the origin are zeroes of this derivative...

Likewise is wrong...you seem to have some problems with partial derivatives. Check this.

Tonio
Step 3

so critical points are (0,0), (1,0), and (-1,0)

Step 4

Step 5

at (0,0):

at (1,0):

at (-1,0):

Therefore, f has a local minimum of 0 at (0,0) and saddle points at (1,0) and (-1,0).

The answer is correct but the work makes no sense. When computing

,

was completely neglected.

should have been:

Same problem with

Is there something wrong with the solution or am I doing something wrong?

Thanks in advance!