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

Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: xy Prove that the function f(x, y) is differentiable everywhere in its do- x² + y? main.

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Q: About what point is the local linear approximation l(x): of the function f(x) = tan x valid? 4

A: According to question, Local linear approximation,lx = x2 +π4-12,         .......1Given Function,fx…

Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

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Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

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Q: x² iy? Find points where f'(z) exist x+y Given f(z) %3D x+y

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Q: What is the formula for the linearization of a function f at the point x = a? %3D

A: Given :To provide the formula for linearization of a function f at the point x=a

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

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Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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Q: Find the linearization of the function f (x) = x at x = 1. L (x) = 固団 Using this linearlization, f…

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Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: Find the absolute maximum and minimum values of f(x,Y) = Zx(y-1) + 7 on the region above the line…

A: We have given f(x, y) = 2x(y - 1) + 7. Method of Lagrange Multiplier:  To find the maximum or…

Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

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Q: What does it mean for a function ƒ(x, y) to be differentiable? What does the Increment Theorem say…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Consider the function f(x) = 3z10 + 3z° – 3z² – 4. Enter the general antiderivative of f(z)

A: Given function is : f(x)=3x10+3x5-3x2-4 We have to find antiderivative(integral) of the given…

Q: Find the maximum rate of change of the the function 80 f(x, y, z) = 1+g² + 2y? + 3z² %3D at the…

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

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Q: express the extreme value theorem for functions of two variables . find the absolute maximum and…

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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: The directional derivative of the function f (x, y, z) = x²z + xyz + y? in the direction of u =…

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

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Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

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Q: The function f(x, y) = 1 + x² + y² at the point (0,0) is local max صواب İhi

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Find the absolute maximum and minimum of the function f(x,y) = 2x² - 4x + y² - 4y +6 on the closed…

A: Given that a function f( x , y ) =2x2-4x+y2-4y+6  on the closed triangular plate bounded by the…

Q: The gradient of f(x, y) xy at (x, y) = (– 1, 1) is

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Q: Find the critical point of the function f(x, y) = V 8x2 + 5y2 . Determine whether it is a minimum,…

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Q: Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at the point P(5, 0). 1. max slope 20T 2.…

A: Given:- f(x, y) = 4 sin(xy) To find:- Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at…

Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

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Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. f(x,y) = x4 - 4xy +…

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Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: Disccus the hatural of the Critical points: f(x,y) = 3xy-x²-y?

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Q: Suppose f and g are two differentiable functions such that f(9(x)) = x? and supposed the equation of…

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Q: Find the critical point of the function f(x, y) = 9x 3y- - In(\r+ y|). c = || Use the Second…

A: Let f(x,y) be any function of two independent variables x and y supposed to be continuous for all…

Q: Solve this attachment.

A: Given:fx,y=xy2-x2-y

Q: Show that f(z) = x³+i(1−y)³ is differentiable only at x = 0, y = 1 and f'(z) = 0.

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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: Find the critical point of the function f(x, y) = 24x – 4y² – In(|x + y|). - - c = Use the Second…

A: see below the answer and explanation

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: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: The average revenue is defined as the function R(x) Ř(z) (x > 0) Prove that if a revenue function…

A: Let Rx denotes the revenue function. The average revenue function is defined by Rx=Rxx where x&gt;0.…

Q: The average revenue is defined as the function R(x) R(z) = (x > 0) Prove that if a revenue function…

A: Given average revenue defined as function R¯x=Rxx   x&gt;0 To prove if a revenue function Rx is…