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Suppose that f(x,y)=-2x3 - 7 xy + 8y2, (-0.5104, 0.2233) is a critical point, 1 xx...
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:
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)
15. Find the critical points of the function f(x, y) = y3 - 6y? - 2x3 - 6x2 +48x+20. Then, use the Second Derivative Test to determine whether they are local minima, local maxima, or saddle points. Find local maximum and local minimum values. (10 Pts) 16. Use Lagrange multinliers to find the maximum
3. (28 points) Let f(x,y) = 2x3 - 6xy+3y- be a function defined on xy-plane. (a) (6 pnts) Find first and second partial derivatives of f. (b) (10 pnts ) Determine the local extreme points of f (max., min., saddle points) if there is any. (C) (12 pnts) Find the maximum and minimum values of f over the closed region bounded by the lines y = -x, y = 1 and y=r
3 Ltuts.),)wher F.,and v are differentiable. Suppose also that (-2-)1 (-2-3)--101, u (-2-3)-4, x (-2-3)--5 F (L-7)-3, F(-2-3)-3, F(I.-7)-2, and F.(-2-3)-0. Find W (-2-3 Circle your answer below o w(-2-3)-2 (e) W(-2-3)-12 ( W(-2-3)-14 (g) W(-2-3)-35 (h) W (-2,-3)-199 W(-2,-3)-202 M x2 + xy + y2 + 3y the local maximum and minimum values of the function f(x,y) 4. Find . Circle your answer below. (a) Relative minimum f(1.-2)--3, and no relative maximum. (b) No relative minimum, and relative maximum...
Problem 8. (1 point) For the function f(x,y) = 4x² + 6xy + 2y”, find and classify all critical points. O A. (0,0), Saddle O B. (4,6), Saddle O C. (4,6), Relative Minimum OD. (0,0), Relative Minimum OE. (0,0), Saddle |(4,6), Relative Maximum
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.
please solve all parts. For the function f(x,y)=x3+y3 – 6y2-3x+5, do the following: (a) Determine its critical point(s) if exists. Express your answer as coordinate pairs with parentheses and commas. Separate your answers with commas and list in ascending order of x if the function has more than one critical point. Use **DNE" if the function has no critical point. Answer: (b) Use the D-Test to classify at each critical point whether the function has a relative maximum or minimum,...
Suppose that f(x,y)=xy. Find the maximum value of the function if x and y are constrained to sum to 1. b) How can you be sure this is a maximum and not a minimum?
Consider the following function. 8(x,y) = -372 – 8y2 +6V8x (a) Find the critical point of 8. If the critical point is (a,b) then enter a,b (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a,b) from the Second Partials test that is used to classify the critical point. (e) Use the Second Partials test to classify the critical point from (a).