Find all the local maxima, local minima, and saddle points of the function.
3
f(x,y) = x\textsuperscript{3} - 18xy\textsuperscript{3}
Identify the partial derivatives, f\textsubscript{x}(x,y) and f\textsubscript{y}(x,y).
f\textsubscript{x}(x,y) =
f\textsubscript{y}(x,y) =
Identify the second derivatives, f\textsubscript{xx}(x,y), f\textsubscript{xy}(x,y), and f\textsubscript{yy}(x,y).
f\textsubscript{xx}(x,y) =
f\textsubscript{xy}(x,y) =
f\textsubscript{yy}(x,y) =
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
?A. A local maximum occurs at
(Type an ordered pair. Use a comma to separate answers as needed.)
The local maximum value(s) is/are
(Type an exact answer. Use a comma to separate answers as needed.)
?B. There are no local maxima.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
?A. A local minimum occurs at
(Type an ordered pair. Use a comma to separate answers as needed.)
The local minimum value(s) is/are
(Type an exact answer. Use a comma to separate answers as needed.)
?B. There are no local minima.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
?A. A saddle point occurs at
(Type an ordered pair. Use a comma to separate answers as needed.)
?B. There are no saddle points.
