Is My Calc 3 Homework Solution Correct?

[algar32]

Calc 3 tough! not sure if right.

Homework Statement

Can you check if this is right?
Let f(x,y) x^(2)y-3x^2-2y^2+11y+5
1. find all critical points of f(x)
crits at (0,11/4), (-1/3),(1/3)

2. determing nature of the crit points you found
D(-1,3) saddle
D(0,11/4) max
D(1,3) saddle

3. find the extreme values of f(x) on the closed region bounded by y=X^3 and y=4.
global min a f(0,0)=5
global max at f(-2,4) and f(2,4) =21

Sorry for the briefness. I wrote this out for the second time because it unlogged me in after I typed it all in and the brower ate my document :(.

Homework Equations

The Attempt at a Solution

 

[lippyka]

Your answers look correct. The only thing I would suggest is that you include more detail in your explanations, such as how you determined the nature of each critical point and the extreme values of f(x).