Determine and distinguish the stationary values of the function f(x, y} = x² – 6x² – 8y². -

Q: Find the gradient of the function f(x,y) = 4y - 9x at the point (9,3). Then sketch the gradient and…

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Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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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: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) =

A: Topic = Functions

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 4, (1, 2) Vf(1, 2) =

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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: Find the gradient of the function at the given point f(x, y) = 5x + 4y² + 1, (1,4) Vf(1, 4) =

A: Solution of given question is written in below steps.

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 f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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Q: Find the linearization of the function f(x,y) = V9x² + 16y² at the point (1, 1), and use it to…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

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Q: Find all stationary points of the function z = f(x, y) = 3x² – 6xy + 2y³.

A: To find stationary points of the function z=fx,y=3x2-6xy+2y3

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

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z)…

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 3y2 + 2, (3, 5) Vf(3, 5) =

A: Given: fx,y=2x+3y2+2 ; Px,y=3,5   As we know that; The expression for the gradient vector.…

Q: Let f(x, y) = xe*Y. Find the maximum rate of change of f at the point (2, 1). хе

A: We will find the maximum rate of change.

Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: If Wly, Y2 Y3]= 0, then (y1, y2, y3) must linearly dependent, where y1, y2 , y3 are diffferentiable…

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Q: 7. Find and classify all stationary points of the function f(r, y) = 1 +y? - 12r + 6y-3

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Q: Find the derivative of the function. g(u) = (8+ u²)*(1 – 5u²)8 %3D = (n), 6

A: Now we will differentiate g with respect to  u . And we will  derivative the function using chain…

Q: Find the linear approximation of the function y = x at point xo = 1 .3 О а. у%3D Зх - 2 О Б. у3D 3х…

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Q: Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

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Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Find the coordinates of the point(s) at which the curve y = x-2/3 has gradient – 1/6. %3D -

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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Q: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

A: What is the domain of the function w = ƒ(x, y, z) = 1/xyz?

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Consider the function f(x, y) = xª + y4 – x² – y? – 2xy. Find its stationary points. Show that one…

A: Given :

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y² + 4, (3, 4) Vf(3, 4) =

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Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: · y = Vx - x, (1, 0)

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

A: We have to solve

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: Find and determine type of stationary point for f(x,y)= 2x² – 4.xy + y² +x+3y

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Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

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Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Consider the function f: R²R given by f(x, y) = ³ + ² + 2xy + y2-y. Find and classify all stationary…

A: Here is the solution:

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

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Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…

Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

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