Mixed Partial Derivatives
Example where the mixed partials are not equal
Courtesy of Professor Tom Vogel of Texas A&M University
Local Extrema (Max/Min)
a graph with a local maximum
graph of 9-x
^{2}
-y
^{2}
with a critical point at (0,0)
a graph of a saddle
graph of y
^{2}
-x
^{2}
with a critical point at (0,0)
a graph of a monkey saddle
graph of (1/3)x
^{3}
-xy
^{2}
with a critical point at (0,0)
this is an example of a degenerate critical point at (0,0)
a graph of a function with two critical points
graph of y-(1/12)y
^{3}
-(1/4)x
^{2}
+(1/2)
this example has two critical points---one local max and one saddle