This two-variable function has exactly two critical points, including the origin: 43 13 f(x,y) = xy...
Let f(x,y) = 4 + x² + y² – 3xy f has critical points at 10,0) and (1,1) use the second derivative test to classify these points as local min, local 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.
consider the function f(x,y)=x^2-2xy+3y^2-8y (a)find the critical points of f and classify each critical point as local max min or saddle point (b) does f have a global max ?if so what is it ? does f have a global min ? if so what is it ?
Given a two-variable function f(x, y), if P(x0,yo) is a critical point, then the behavior of f around P can be approximated by its second order terms according to Taylor series, that is, f(x,y) = f(P) + F(x – xo)?H (x, y) , where H(x, y) = fyy(P)(=%)2 + 2 fxy(P) (?=%) + fxx(P). (a). If H(x, y) > 0 for all x,y, is P a local max, local min or saddle point? (b). Let s = (4=90). Then, H(x,...
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.
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.
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
QUESTION 7 Find all the critical points for f(x,y)=-x® + 3x - xy and classify each as a local maximum, local minimum or a saddle point. (9 marks)
Suppose f(x,y)=xy(1−10x−4y)f(x,y)=xy(1−10x−4y). f(x,y)f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, determine whether the critical point a local maximum, a local minimim, or a saddle point. First point (____________,__________) Classification: Second point(__________,__________) Classification: Third point (___________,_________) Classification: Fourth point (__________,_________) Classification:
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.