Fid the critical pts of the fnetion and determite whether cach critical point cotesponls to a...
Question 6. (20 pts) Find the critical points of S(,y) = x4 + 2y2 – 4cy. Then use the Second Derivative Test to determine whether each critical point is a local min, max, or saddle point.
Question 6. (20 pts) Find the critical points of f(x, y) = x4 + 2y2 – 4xy. Then use the Second Derivative Test to determine whether each critical point is a local min, max, or saddle point.
Question 6. (20 pts) Find the critical points of f(r,y) = x4 + 2y2 - 4xy. Then use the Second Derivative Test to determine whether each critical point is a local min, max, or saddle point.
4. Consider the following function in R" f(Fi, n)=-1) k-1 Find the critical point of this function and show whether it is a local minimum, a local maximum, or neither 5. By examining the Hessian matrix, show that if f(x,y, ) has a local minimum at then g(z, y,) -f(x,y, ) must have a local maximum at that point. Likewise, show that if f has a local maximum, then g must have a local minimum at that point. (ro, yo,...
find the critical points of f(x,y)=2x/81+x^2+y^2 to determine whether each critical point is a maximum, minimum, or saddle point.
9. (10 pts.) The following function has three critical points (0,0), (1,1), (-1,-1). Use the second derivative test to determine if each point is a local maximum, local minimum, or saddle point. S(1,y) = 1 + y - 4xy +1.
Problem 10 [10 pts] Determine whether cach of the following series is convergent or divergent, You must justify your conclusions by identifying the test used. (a) (b) + 13 - 12X-7 13 1 (lan
(c) Determine the critical points of the functions below and find out whether each point corresponds to a relative minimum, maximum, saddle point or no conclusion can be made. f(x,y) = 3xy - x - y (7 marks)
Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. .f(x, y) = x²y2
Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. f(x, y) = x2 + 4xy + y21