By examining the behavior of ( f ) on the lines ( x = 1 ) and ( y = x ) that pass through ( (1, 1) ), explain why ( (1, 1) ) is a saddle point. (It turns out that ( (3, 3) ) is a local minimum.)
a) Because the function's values decrease along ( x = 1 ) and increase along ( y = x ) near ( (1, 1) )
b) Because the function's values increase along ( x = 1 ) and decrease along ( y = x ) near ( (1, 1) )
c) Because the function's values increase along both ( x = 1 ) and ( y = x ) near ( (1, 1) )
d) Because the function's values decrease along both ( x = 1 ) and ( y = x ) near ( (1, 1) )