Use the Second Derivative Test to determine the relative extremum trema) and saddle point(s), if any, for the function defined by f(x,y) = xy –

Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

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Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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Q: S(r) = In (r² + 2x + 5)

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Q: . Find all critical points of the function f(x, y) = xy + x – y and classify them as loca maxima or…

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Q: Find the derivative of the function f(x,y,z) = x² + 2y² – 3z² Po = (1,1,1) in the direction of at…

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Q: ) Find any relative(local) extrema and saddle points of f(x,y)=xª+yª-4xy+1.

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Q: Determine the critical points of f(x, y) = 4.xy-a -y". Then, using the Second Derivative Test,…

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Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

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Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

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Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True B)…

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Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

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Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use…

Q: f (x, y) = 3xy(x + 2y – 6) -

A: By second derivative test ,

Q: Let f(x, y) = V xy. Find the derivative of f. af 1 ду 2

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Q: Find the orthogonal trajectories of the family of curves x when 'a' is the parameter. +y Da

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Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

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Q: Find the derivative of f(x) at r = 0 using the definition of the derivative as a limit. %3D Va +I

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Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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Q: The partial derivative of function respect to y* f(x, y) = x² + y/y? %3D

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Q: Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameter

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Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),…

A: Given that      f(x,y,z)=ln(x2+3y2+9z2), P0(3,3,3), u=3i+4j Here we have to find the derivative of…

Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=3 ex cos (yz), Po(0,0,0),…

A: Solution: f(x,y,z) =3exCos(yz) P0=(0,0,0)

Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

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Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

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Q: Determine and classify all relative extrema and saddle points of f(x, y) = 2ry using the Second…

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Q: Determine the derivative of the function defined by h(x, y) = Arctan () + v3Arcsin () %3D at the…

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Q: Find the gradent of x, y)-- and the largest value of the directional derivative of fx y can have at…

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Q: Find the critical point of the function. Then use the Second Derivative Test to determine whether it…

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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: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

A: Consider the provided information, fxx0,0=5,fyy0,0=3  and fxy0,0=-4 The Second Derivative Test to…

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = xy + yz + zx, Po(1,…

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Q: Examine the function f (x, y) = x3 − 6xy + y3 for relative extrema and saddle points.

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Q: Find the derivative of the function at Po in the direction of u. x- 5y g(x,y) = Ро(1, - 1), и%3 3і +…

A: To find the derivative of the function  g(x,y)=x-5y5xy+7 at P0(1,-1)in the direction of…

Q: Evaluate the required second order partial derivative. Find fxy(5,-1), if f(x,y)= -2xe5y

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Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Find the derivative of the function at Po airection oT u. f(x, y) = 3x 2 + 4y, P o(8, 7), u = 3 i -…

A: 1. Given f(x, y) = 3x2 + 4y and u = 3i - 4j u^ = 1|u|u = 15(3i - 4j) ∇f·u^ = (i^ddx(3x2+4y) +…

Q: Find the critical point of the function f(x, y) = x² + y – ry + 7.5x C = Use the Second Derivative…

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Q: Find the derivative of f(x, y) = (2x – y°, sin(ry), r²y*)

A: Given f(x,y)=2x-y3,sin(xy),x2y3 differentiate f(x , y) with respect to x we get…

Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

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Q: C. Find all critical point (s) of f and use the Second Derivative Test to determine whether f has…

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Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

A: Maxima or minima: Let f(x, y) is any function. 1) Evaluate fxx, y=0 and fy0,0 for critical point. 2)…

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = xy + yz + zx, Po(1,…

A: Given query is to find direction derivative.

Q: Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) =…

A: Given that, ƒxx(0, 0) = -6  ƒyy(0, 0) = -3 ƒxy(0, 0) = 4

Q: Find the Partial derivative of f with respect to y for * f (x, y) = x+y

A: →While calculating ∂f(x,y)∂y , consider 'x' as constant.→∂∂yuv = v∂u∂y-u∂v∂yv2