Consider f(x) = x4 – 8x3 + 18x². Investigate convexity/concavity, find all the inflection points.

Q: Find all points (x.y) where f(x.y) may have a maximum or minimum. f(x,y) = - 3x + 5xy- 2y² +x+y

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Q: Find the relative maximum and minimum values. =x2 + y² - 6x + 12y - 9

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Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Suppose that f(x, y) = 4x* + 4y* – xy Then the minimum is

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Q: Consider a manufacturing firm that occupies one hectare of land. The firm trans- ports over half of…

A: According to the given information, it is required to draw the firm’s bid rent curve for x=0 to…

Q: At what interval is y=x^3-3/2x^2 concave upward?

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Q: Find all points on the curve 5x² + 8y² = 64 %3D

A: Given: The curve 5x2+8y2=64 where tangent line passes through the point (11, 0). To find: All the…

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

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Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Examine for minimum and maximum values of f(x,y,z)=2xyz-4xz-2yz+x^2+y^2+z^2-2x-4y+4z

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Q: What is the maximum value of the function f(x, y) = 4 – x² – 2y? subject to the constraint 2 + y? =…

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Q: Find the relative maximum and minimum values. f(x.y)= 8xy-x - 4y

A: Given :f(x,y)=8xy-x3-4y2

Q: find the orthogonal trajection of the family of curves x2+y2=a2

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Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

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Q: Determine the convexity/concavity property of the following: (ii) f (x, y) = 2x² – y?

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Q: Suppose that f(x, y) = 3xª + 3yª – 2xy Then the minimum is

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Q: Suppose that f(x, y) = 3x* + 3yª – 2ry Then the minimum is

A: Given, f(x,y)=3x4+3y4-2xy

Q: Is 6y-y^2 a convex function

A: Given:  Let fy=6y-y2  To Find: To check the given function for a convex function.

Q: Find the local minimum value of f(r, y) = 4 + x7 + y7 – 7ry.

A: We have to find the local minimum of the function f(x,y).

Q: Use LaGrange multipliers to find the maximum and minimum for the function f(x, y)=x² +2y² restricted…

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Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

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Q: at what interval is  y=3x^5-5x^3 concave upward?

A: Given y=3x5-5x3

Q: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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Q: Suppose that f(x, y) 3x + 3y* 2xy Then the minimum value of f is

A: We have to solve given problem:

Q: Find the maximum value of f(x,y) = 25 - x - y on the line x+ 4y = 17. %3D

A: First-order derivative test for Maximum value : - The slope of a function is determined by its first…

Q: Find the local minimum value of f(æ, y) = 4+17 +y17 – 17ry.

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Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: Find the absolute maxima and minima of f(x, y) = 3x2 + 10y on the closed triangular region bounded…

A: Consider the equation

Q: Determine the maximum and minimum values of f(x,y,z) = 3x + 6y + 2z, subject to 2x^2 + 4y^2 + z^2 =…

A: Using the lagrange multipliers

Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

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Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: Find the orthogonal trajection of the family of curves x2+y2=a2

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Q: Find the maximum value of 5x2 - 4xy+ 8y subject to x+y? = 1..

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Q: Consider the function of y = 5x + 2x- 3x and find the maximum and minimum points.

A: Without wasting any time, differentiate the function w.r.t x on both the sides, dy/dx = 15x2 + 4x -…

Q: Find the relative minimum f(x,y)=288y2+x2-x2y

A: According to the given information it is requires to find the relative minimum of the function:

Q: Find the extreme values of f(x, y) = x² + y² subject to the condition x²y = 1 using Lagrange…

A: solution is given below..

Q: Use Lagrange multipliers to find the highest and the lowest points on the curve of intersection of…

A: Here we have to find the maximum and minimum value of z=x2+4y2 subject to constraint x2+y2=1.

Q: Find all critical points of f(x,y) = y²x – 2x² – y² and classify them as relative minima, relative…

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Q: Q.2/ Test the following surfaces for maxima, minima and saddle point:- Z(x,y) = xy + 7x- 12y'x-6x +5

A: z=(x,y) 1. Zx=∂f∂x=fx=0Zy=∂f∂y=fy=0this will give us the critical point (a,b)Now find…

Q: Find the local minimum value of f(r, y) = 4+ a7 + y7 - 7ry.

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Q: find the points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…

Q: Q.2/ Test the following surfaces for maxima, minima and saddle point:- Z(x.y) = xy + 7x – 12y°x² –…

A: Given, Surface is Z(x,y)=xy+7x2-12y2x2-6x+5 If rt-s2>0 and r>0 then the function has minimum…

Q: Use langrage multiplier to maximize f(x,y)=25- x2 -y2 subject to 2x+y=10

A: We have f(x,y) = 25 -x2 -y2 subject to 2x + y =10

Q: Use Lagrange multipliers to find the point on the circle x2 + y2 = 1 which is (a) closest to and (b)…

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Q: Find the critical points of the function f(r, y) = 8y3 +12x2 – 24ry and classify them as local…

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Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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Q: Compute the length of the curve: f (x) = x² 2x, 0<x<2

A: Given:- f(x) =x2 -2x  To find:-  Length of curve over interval [0, 2]

Q: Find all the relative extremum points and saddle points of f(x, y) = y* – 2y²x – x² + 4x |

A: given functionf(x,y)=y4-2y2x-x2+4x suppose that (x, y)=(a, b) is a critical point of f(x, y)and D(x,…