Let f(x, y) = x²-y³ + 18xy List the critical points: (0,0) The critical point at the origin is a saddle point The critical point with negative y value is a minimum Submit Question *

How are the absolute maximum and minimum similar to and different from the local extrema?

Let f(x,y)=y22x2y+4x3+20x2. The only critical points are (2,4), (0,0), and (5,25). Which of the following correctly describes the behavior of f at these points? Source: Society of Actuaries. a. (2,4): local relative minimum (0,0): local relative minimum (5,25): local relative maximum b. (2,4): local relative minimum (0,0): local relative maximum (5,25): local relative maximum c. (2,4): neither a local relative minimum nor local relative maximum (0,0): local relative maximum (5,25): local relative minimum d. (2,4): local relative maximum (0,0): neither a local relative minimum nor local relative maximum (5,25): local relative minimum e. (2,4): neither a local relative minimum nor local relative maximum (0,0): local relative minimum (5,25): neither a local relative minimum nor local relative maximum

Find all points where the functions have any relative extrema. Identify any saddle points. f(x,y)=x2+xy2x2y+2