(1) Where on the line r = ay does the function f(x, y) = (x – a)² + (y – 2)2 attain its smallest value?

Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d.…

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

A: To find critical point in which given function has relative maximum and minimum.Where…

Q: The function f defined by the rule f(z, y) = In(xy) increases fastest in the direction of T. F (1,…

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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

A: We have, To find the critical point, we have to take the partial derivative of the function, and…

Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: 1. Find the critical points of the function 2 f(x, y) = x² + 4xy.

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

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: Determine two functions, defined on the interval  ( − ∞ , ∞ ) , whose Wronskian is given by  W ( f 1…

A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: The functions f (x, y) = x^2 + y^2 and g(x, y) = x^2 − y^2 both have a critical point at (0, 0). How…

A: We have given functions fx,y=x2+y2   and gx,y=x2-y2 We have given 0,0 is a critical point of these…

Q: 1 A point is moving along the graph of the functiony = dy 9x2 + 6 such that dt = 3 centimeters per…

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Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

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Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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Q: Show that (0,0) is a critical point of f(x,y) = x + kxy + y no matter what value the constant k has.

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Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

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Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

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Q: Find the critical point of the function: f(x, y) = 4x2 + 2y2 − xy + x

A: we have given a function f(x, y)  We have to find the critical point

Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

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

Q: 2 3 tegral of the function xy d by x = 0, y = 0, z = C %3D %3D (2(5)

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Q: How can we minimize the error of an approximation in a linear approximation at the point (a. ƒ (a))?…

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Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

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Q: s of 0 would be a minimum value on the graph of y = sin 0 over the interval [-27,0)?

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Q: Show that f(x,y) = 1-x* - y* has a relative maximum, even though D in the theorem is 0. The critical…

A: Given : f(x, y) = 1 - x⁴ - y⁴

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x² 5x…

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Q: Show that (0,0) is a critical point of f(x,y) = x kxy + y2 no matter what value the constant k has

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Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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

A: Given, f(x)=x6

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: x² + y² F(x, y) =- - is a homogeneous function of degree

A: For finding degree of homogeneous function, Put x=hx and y=hy

Q: -2 In(x) Consider the function f(x, y) 3y

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Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

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Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: 3. Find a linear approximation to the function at the point x = 3. y = f(x) = x²e + 8x

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Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: Where does the function f(x,y)=3 − 10x + 12y − 5x2 − 6y2 have a critical point?

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Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: In Problem (A), Show that f(x, y) is differentiable at the indicated point. A) f (x, y) = (x2 +…

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Q: 2. Determine the critical points of the function: R(y) : y2 – 6y -

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Q: 1, Differentiate the function. (1) f(x)= /32 (2) f(x)= (x°+10) 5 (3) f(x)= 2.x - V х (4) f(x)=…

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Q: The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How…

A: We have f(x, y)=x2 + y2 and g(x, y)=x2 - y2 By finding the partial derivatives fx=2x, fy=2y, gx=2x,…

Q: 1)Classify the critical points of the function f(x,y)=x²+y³+x²y+4

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Q: 9. An equation of the line normal to the graph of f(x)=, at (1,–1) is (a) 2x - y -3 -0 (b) 2x + y…

A: Explanation: Given that  f(x)=xx-2 at (1,-1)   Concept Used: To find the normal firstly find the…

Q: (b) Form the partial equation by eliminating function f from z = f(x?

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