#7 Given f(x,y) = x³y-xy-2x. find and classify (min, maxer saddle) all critical points.

Find two nonnegative number x and y for which x+3y=30, such that x2y is maximized.

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