Question

8) Given f(x,y)= x^3 + y^3 + 9xy + 5. ( Show all work please)

a) Find all the critical points.

b) Give all the local maxima, minima and saddle points.

c) Are the local extrema also global extrema? Explain.

9) You are standing at the point (1,1,3) on the hill whose equation is given by z=5y-x^2-y^2
(assume x,y,a are measured in meters)

a) in what direction (relative to the horizontal plane) should you go to have steepest ascent?

b) What is your initial rate of increase in that direction found above?

c) If instead you decide to go southeast from that (1,1,3) location, will you be ascending or descending? At what rate?

d) In what direction ( relative to the horizontal plane) should you go to maintain your height? (i.e. not ascend or descend).

Answer 1