Problem 3. (10 points) For the function f(x,y) = r? - Ty + y2 – 21+...
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 ?
QUESTION 16 The function f(x,y) = x -x- y2 + 2y has O A. 1 local max. 1 local min. OB. 1 saddle pt. and 1 local min. O C2 local min. OD. 1 saddle pt. and 1 local max. O E 2 saddle pt.
QUESTION 23 The function f(x,y) = x3 – x- y2 + 2y has O A 1 saddle pt. and 1 local min. OB. 1 local max. 1 local min. OC. 2 saddle pt. OD. 1 saddle pt. and 1 local max. O E. 2 local min.
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.
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,...
please show work, im so lost on all of these Given f(x, y) = 4x 5xys + 3y?, find f(x,y) = fy(x, y) = f(x, y) = 5x2 + 4y? $2(5, - 1) = Given f(x, y) = 4x2 + xy 4x² + xys – 67%, find the following numerical values: $:(3, 2) = fy(3, 2) = Given f(x, y) = 3x4 – 6xy2 – 2y3, find = fry(x, y) = Find the critical point of the function f(x, y)...
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.
5. Consider the function f: R -> R given by f (x, y) := e°+v* _ 4. (a) Sketch the level curves of f. (5 marks) (b) Find Vf, the gradient of f, and determine at which points Vf is zero. Remark: These points are called the critical points of f (5 marks) (c) Determine whether the critical points of f are local minima, local maxima, or saddle points by considering the level curves of f. (5 marks) (d) Calculate...
This two-variable function has exactly two critical points, including the origin: 43 13 f(x,y) = xy - Q17.1 FR 5 Part (a) 4 Points Find the second critical point, other than (0,0). Please select file(s) Select file(s) Q17.2 FR 5 Part (b) 4 Points Classify the critical point (0,0) as a local min, local max, or saddle point, using the (multivariate) second-derivative test.
73 Optimizing Functions of Several Variable Problem 6 Previous Problem List Next (2 points) Consider the function f(x, y) = e Ax-x2-6-y Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank fx = fy = fix fxy - fyy The critical point with the smallest x-coordinate is | (local minimum, ) Classification: local maximum, saddle point, cannot be determined) The critical point with the next smallest x-coordinate...