f(r, y) = VI y (c) Prove that the function z-f(x.y) doesn't have any local maximum or minimum in D. Explain the reason.

Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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Q: Find the values of x, y, z at which f (x, y, z) = x2 + 4y2 + 5z2 - 6x + 8y + 3 assumes its minimum…

A: f(x, y, z)=x2+4y2+5z2-6x+8y+3   we have to find all points of x, y, z Taking, ∂f∂x=0, ∂f∂y=0 and…

Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = x² – xy + y² – 5x + 5y…

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Q: 1. The temperature at the point (r, y) on an unevenly heated plate is given by T = f(r, y) = 100+…

A: Given f=100+5x2+15x+10y2gradient of f∇f=∂f∂xi+∂f∂yj     =10x+15i+20yjAt (2, 1)∇f=10x+15i+20yj…

Q: Find the local minimum value of f(x,y) 4x2 + 3y2+ 2x + 2y + 4. Give your answer correct to two…

A: The given function is f(x,y)=4x2+3y2+2x+2y+4

Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: Find the value of the number such that the families of curves  y =(x+c) -1  and y = a ( x+k) 1/3 are…

A: Given,

Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

Q: Is the function f(x, y) = ||x| - |y|| - |x| - |y| differentiable at (0,0)?

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Q: fc is a critical point of F(x), when the is a local maximum or minimum at c? Explain

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Q: Find all points (x, y) where f(x, y) has a possible relative maximum or minimum.

A: We have to find the critical points for the function f(x,y)=-x2+2y2+6x-8y+5.

Q: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

A:

Q: Let f(x, y) = exy and P(1, 0). Find the maximum and minimum rates of change of f at the point P. In…

A: Given function is: f(x,y)=exy and point P(1,0)

Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 2x + 9y < 8. 1. Absolute minimum of f(x, y) is…

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Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-2, 0, 0)…

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Find the absolute extrema of the function on the closed interval. f(x) = 7x² + 2, [-1, 2] -(0,2…

A: The answer is given below:

Q: Groph of f(x)= (x² Is there a Is f differentiable at X=o? Justify %3D sharp Corner at X=O ?

A: Consider the given graph. fx=x2+0.0001 Now, draw the graph.

Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: . Use the second-derivative test for local extrema (: extrema for the function. Identify whether the…

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Q: Find A and B so that f(x, y) = x2 + Ax + y² + B has a local minimum at the point (4, 0), with…

A: Given function of two variables is f(x,y)=x2+Ax+y2+B it has local minimum point at (4,0) and minima…

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: Define the function f: R? → R by f (x, y) = 2xy² – y² – 2x². a) Find the critical points of f. b)…

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Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

Q: Suppose that f(x, y, z) = 2x + 5y + 4z at which a2 + y? + z2 < 12. 1. Absolute minimum of f(x, y, z)…

A:

Q: Find the absolute minimum and absolute maximum of f(x,y)=19−9x+13y on the closed triangular region…

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Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 4x + 7y < 9. 1. Absolute minimum of f(x, y) is…

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Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

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Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

Q: Find the direction at which the function f(x, y, z) = x In(e – xz) increases fastest at (-2, 0, 0)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: prove that xy^2/x^2+y^2 is not differentiable at 0,0 when  xy^2/x^2+y^2 if (x,y) not equal to (0,0)…

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Q: Suppose that f(x, y, z) = 4x + 4y + 3z at which 0 < x, y, z < 5. 1. Absolute minimum of f(x, y, z)…

A: We have to find the absolute minima and maxima.

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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Q: : Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: Consider the function f(x,y) = 3xe" – x³ – e3y. (a) Show that f(x,y) has exactly one critical point…

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Q: Suppose that f(x, y) = x² + y at which 0 < x, y and 3x + 9y < 7. 1. Absolute minimum of f(x, y) is…

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Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Find the point at which the function f(r,y) = 2 in z+2 In y attains a maximum subject to the con-…

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

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 5z) at the point (- 1, 1, 2).

A: We have to find

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: Find the minimum and maximum values of y = V120 - V6 sec e on the interval [0, ] fmin fmax

A: Solve

Q: Find the maximum rate of change of f(x, y, z) = tan(7x + 3y + 6z) at the point (4, – 5, 2).

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Q: Suppose that f(x, y, z) = 3x + 3y + 4z at which a² + y² + . < 52. 1. Absolute minimum of f(x, y, z)…

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Q: Find the point where the maximum value of f(x, y) = xy subject to x + 5y = 74 occurs. (x, y, z) = |

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