This is Section 6.2 Problem 14:
For the function $f(x,y) = x^2 + 4x + xy$, do the following:
(a) Determine its critical point(s) if exists. Express your answer as coordinate pairs with parentheses and commas. Separate your
answers with commas and list in ascending order of $x$ if the function has more than one critical point. Use "DNE" if the function
has no critical point.
Answer:
(b) Use the $D$-Test to classify at each critical point whether the function has a relative maximum or minimum, or a saddle point,
or inconclusive:
At the critical point, the $D$ value is --Select--, and the second order partial derivative $f_{xx}$ is --Select--. Therefore at
this point --Select--
Hint: Follow Example 3.
