Show that the function z = f (x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point. Determine the maximum value

Q: Find all critical points of f(x,y) = 1/x - 1/y + xy and classify each as a relative minimum,…

A: We use second order partial derivative test to find relative maximum and minimum, saddle point

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Q: Find the local maximum, minimum value and saddle point of f(1, y) = x' + y* - 4xy+1.

A: We will use following  critical point ( maximum ,minimum or saddle point ) of a function occur…

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Q: Find the critical points of the function f (x, y) = -x2+ 4xy+ xy2 and determine whether the critical…

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

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Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

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A: To solve the given extrema problem.

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A: Here we use Taylor's approximation.

Q: Use the Second Partial Derivative Test to find all critical points for the following function f(x,y)…

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Q: Find the critical points of f(x, y) = x^3 − y^3 − 3x^2 + 12y + 1 and classify them as a relative…

A: Given the function is fx,y=x3-y3-3x2+12y+1.   Find the partial derivatives.…

Q: Find the local maximum, local minimum and saddle points of the function f (x, y) = y³ + x³ + 6ry.

A: Follow the steps below to yield the result .1. Calculate .2. Find the critical point by solving the…

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A: We need to determine the local maximum and minimum values and saddle points of the function f(x,y) =…

Q: Find all the local maximum, minimum and saddle points for f(x,y) = x³ – 3x + 3xy²

A: Suppose that a,b is critical point of fx,y and its second order partial derivative is continuous…

Q: Consider the function f(x, y) = 3x³ + 3xy² - 18x - y² Compute the stationary points of the function…

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Q: ) Find the local maximum, local minimum and saddle points of the function f (x, y) = x3 + y3 + 3xy:

A: solution of the given problem is below ...

Q: The nature of the stationary point (0, -1) for the function f(x,y), if f= 4-12x, fy= 0 and fry=-4+…

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Q: Consider the function f(x, y) = xy² exp xp ( - 1/3² + y) Compute the stationary points of the…

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Q: 2. Find the critical points of f(x, y) = x³ + y³ – 3x? – 3y + 10 and classify each of them as a…

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Q: Find all critical points of f(x, y) = 2y* + x² – 6xy and classify each critical point as a local…

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Q: 3x4 – 4x3 – 12x² + 18 f(x, y) = 12(1+ 4y²)

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Q: Find the relative maximum or minimum value (if any) of f(x, y) = (x2 + y)ey/2

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Q: Consider the function f(x, y) = 2x³y² − 9x²y² + 12xy² + y Compute the stationary points of the…

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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: Determine the relative extrema and saddle points of the function f(x,y) = 2x2 + 2y2 - 4x -4y +xy

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Q: Find all critical points of f and use the second partial derivative test to determine if there exist…

A: find critical points by putting fx and fy = 0

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A: Given: fx,y=2x4+2y4-xy We need to find the minimum value of the given function.

Q: Find the local maximum and minimum values and saddle points of f(x; y) = (x2 - 2y2).ex-y.

A: For finding local maxima and minima.  D= fxx ×fyy - fxy 2 if D>0 then it is local minima  If…

Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

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Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: Show that the function z = f(x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given a function in two variablesz=fx,y=x3-3x2-4y2+2

Q: Determine the critical point and its type of function f with f (x, y) = 3x^2y + y^3 − 3x^2 − 3y^2 +…

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Q: Let f (x, y)= 3xy² – 2x’y+36xy be a function of two variables and there exist a saddle point at…

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Q: Consider the function f(x, y) = -x²y² + 4y¹ + 4x² Compute the stationary points of the function f(x,…

A: Given function is fx,y=−x2y2+4y4+4x2. We have to compute the stationary points o the function fx,y…

Q: ) Use the second derivative test to classify each critical point of f (x,y)=-x' +4xy- 2y² +1 as a…

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Q: Consider the function f(x, y) = xy² exp ( - 1/² + y ) 3 Compute the stationary points of the…

A: Given fx,y= xy2exp-x33+y

Q: Find the maximum and minimum values of f(x,y) =xy constrained on x2+2y2=1

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Q: Find the local maximum minimum values and saddle point(s) of the function S(r, y) = 9 – 2x + 4y – a²…

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Q: f(xiy)=4+x+y? Ixy

A: In the given question we have to find the local extrema and saddle point of the function f(x,y) s.t…

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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Q: Find all the relative extremum points and saddle points of f(x, y) = y* – 2y²x – x² + 4x |

A: given functionf(x,y)=y4-2y2x-x2+4x suppose that (x, y)=(a, b) is a critical point of f(x, y)and D(x,…

Q: Consider the function f(x,y) = (3x^2 + bx)(2y^2+dy) where b and d are non-zero constants. Determine…

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