Q.2/ Test the following surfaces for maxima, minima and saddle point:- Z(x.y) = xy + 7x – 12y°x² – 6x + 5

Q: Consider 2 2.4 3 f(x) 0.8 5.5 Find the curve fitting y(x)- Ax + B

A: Let's Solve,

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A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

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A: see below the answer and calculation

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A: Here we have to use the Lagrange multiper method

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

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Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

A:

Q: Q.2/ Test the following surfaces for maxima, minima Z(x,y) = xy + 7x² – 12y°x² – 6x + 5

A: Given           Z(x,y) = xy+7x2-12y2x2 -6x+5   ...   (1)

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

A:

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A: Let's find lowest and highest temperature by using langrange multipliers.

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Q: Use the Lagrange multiplier method to find the maxima and minima of the function f(x, y) = xy on the…

A: Consider the given function fx,y=xy and let gx,y=3x2+y2-6. Using Lagrange multipliers,…

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A: Solution of the problem as follows

Q: Test the following surface for maxima minima and saddle point Z= 5+xy+x²+2y+3x

A: First we will find the gradient of the given function using the gradient we will find the critical…

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A: Given:

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A: We will use second derivative test to find the smallest distance among point (5,0) and curve

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Q: Picture attached. Thanks in advance!

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Q: Use Lagrange multipliers to find the minimum distance from the Curve Point Parabola: y = x² (0, 3)

A: Given: The parabola y=x2 and indicated point is 0,3 Formula for the distance is d=x1-x22+y1-y22…

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A: It is length of curve.

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A: solution is given below..

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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…

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A: x - y2 = 0 x = y2  Let us take a point (x,y)=(y2, y) on the parabola

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…

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Q: Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

A: We need to find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

Q: Q:1) A) Test the following surface for maxima minima and saddle point Z= 5+xy+x²+2y+3x

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A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

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

A:

Q: 6. Find the maxium andd minimum values of the following functions by using Lagrange Multiplier. a)…

A: We need to find the maximum and minimum value of the function subject to the given constraints.…