Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x + xy + 2x + 2y + 1 Select

Find all the local maxima, local minima, and saddle points of the function. 

f(x,y) = x² + xy + 2x + 2y + 1 

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