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-x²-y² with a critical point at (0,0)
• a graph of a saddle
  graph of y²-x² with a critical point at (0,0)
• a graph of a monkey saddle
  graph of (1/3)x³-xy² 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)y³-(1/4)x²+(1/2)
  this example has two critical points---one local max and one saddle