5xy has five criticial points, one is at the origin, and one lies in each of ez+ y? The function f(r, y) the four quadrants of the xy-plane. Find and classify each critical point. (a) This critical point at (0,0) is a Relative Maximum Saddle Relative Minimum (b) The critical point in Quad I is at (x, y) = . This critical point is a Relative Minimum Relative Maximum Saddle (c) The critical point in Quad Il is at (r, y) = . This critical point is a Relative Minimum Relative Maximum Saddle (d) The critical point in Quad IIl is at (x, y) = . This critical point is a Relative Minimum Relative Maximum Saddle (e) The critical point in Quad IV is at (x, y) = . This critical point is a Relative Maximum Saddle Relative Minimum

Q: Use the second derivative test to identify any critical points and determine whether each critical…

A: Given:- F(x, y) = -x3 +4xy -2y2 +3 To find:- Maximum, minimum and saddle point of given function

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Q: If (2/3,1/6) is a critical point of f(x, y) = x2 - In(x) + xy - 2y'then (2/3,1/6) is: a saddle point…

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Q: J(*, Y) nas fiv polhts, ohe ne origin, and ohe lles lh e ez² + y? of the four quadrants of the…

A: To find the critical points first we find partial derivatives and then put it equal to z zero  As…

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Q: If (2/3,1/6) is a critical point of f(x, y) = x2 - In(x)+ xy – 2y then (2/3,1/6) is: a saddle point…

A: f(x,y)=x2-ln (x)+xy-2y2 has a critical point 23,16

Q: If (2/3,1/6) is a critical point of f(x, y) = x² – In(x) + xy - 2y²then (2/3,1/6) is: a saddle point…

A: We are given : f(x,y)=x2-ln(x)+xy-2y2 ⇒fx=2x-1x+y⇒fy=x-4y⇒fxx=2--1x2=2+1x2⇒fxy=1⇒fyy=-4

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A: Calculate the value of D and then decide the nature of critical point.

Q: The critical point of f(x,y)=4x2+5xy+3y2 is the point (0,0).  Classify this critical point:…

A: To categorize the e critical point of f(x,y) at point (0,0) using second derivative test.

Q: Find and classify all critical points of f(x, y) = x3 +y3 -x² -y? + 20y + 10. (Order your answers…

A: we find all critical point offx,y=13x3+13y3-12x2-92y2+20y+10

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A: We have to solve given problems:

Q: If (2/3,1/6) is a critical point of f(x, y) = x2 – In(x) + xy - 2y'then (2/3,1/6) is: a saddle point…

A: We are given : f(x,y)=x2-ln(x)+xy-2y2 ⇒fx=2x-1x+y⇒fy=x-4y⇒fxx=2--1x2=2+1x2⇒fxy=1⇒fyy=-4

Q: 1- If the critical point of the function f (x, y) = xy - x? - y? - 2x- 2y +4 is (-2,-2), this point…

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Q: If (2/3,1/6) is a critical point of f(x,y) x2- In(x)+ xy-2y2then (2/3,1/6) is: a saddle point D a…

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y) = x2-ln(x)+xy-2y2 as follows.  f(x,y) =…

Q: 7. Determine whether there is a relative maximum, a relative minimum, a saddle point, or…

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A: The detailed solution is as follows below:

Q: If (2/3,1/6) is a critical point of f(x, y) = x2- In(x) + xy- 2y then (2/3,1/6) is: a saddle point a…

A: Given that (2/3,1/6) is a critical point of f(x,y)=x2-ln(x)+xy-2y2. We need to find the nature of…

Q: Consider (x, y, z) = x² + y² + z² + 2xyz. Show that (0,0,0) and (-1, 1, 1) are both critical points.…

A: Here we solve the given calculus problem.

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A: For the solution follow the next step.

Q: Using these equations 8x+2xlambda=0 4y+2ylambda=2 x^2+y^2=2y Find x, y, critical point,…

A: 8x+2xlambda=0 4y+2ylambda=2 x^2+y^2=2y

Q: 5. Find the critical point and determine whether local maximum or minimum: y = e" + e-2aæ

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Q: Let f (x, y) = (4xy – 2)3 + e2x, then find: f.ry(1,–1)

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: What is the best description of point (0, 0) on the plot C) above? (i) Local minimum (ii) Local…

A: At point (0,0) As we move in +ve x -direction, from x = (-2,2) and keeping y = 0.For x(-2,0) :…

Q: The point (0, 0) is a critical point for g(x, y)=4+x³ +y³- 3xy. Then at (0, 0), g(x, y) has a O…

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Q: 6. Determine a, b, c and d so that the curve y = ax3 + bx2 + cx + d so that the curve will have a…

A: Note: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should…

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Q: 18. Find all critical points of f(x, y) = In(x+y) +x² – y +1 and classify each critical point as a…

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Q: i. Discuss and sketch the curve x² + 6 x = -8 y – 25 ii. For the curve y = x3 – 6 x2 + 10 - (a) Find…

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Q: 3] If the critical point of the function f (x,y) = 10 xye-(x²+y') is (,). test this point %3D…

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