Find the absolute minimum and absolute maximum of f(x,y)=3−10x+13y on the closed triangular region with vertices (0,0),(13,0) and (13,16). List the minimum/maximum values as well as the point(s) at which they occur. If a min or max occurs at multiple points separate the points with commas.

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: Compute the abscissa of the minimum point of the curve  y = x3 - 12x -9.

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Q: Use the method of Lagrange multipliers to find the minimum distance from the origin (0, 0) to the…

A: We need to use the method of Lagrange's multiplier to determine the minimum distance from the point:…

Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: Consider the function f(x,y) = y6 — 6x²y² + 3x4 Compute the stationary points of the function f(x,…

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Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

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Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: Examine for minimum and maximum values of f(x,y,z)=2xyz-4xz-2yz+x^2+y^2+z^2-2x-4y+4z

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Q: Let f(x, y) = x4 +y² – y – 4.x². Find and classify all the critical points (whether they are points…

A: We have to find

Q: Find the absolute maximum of f(x,y) = 7x²y² + 5y² + 9x² bounded by y = x, y = 0 and x = 2.

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Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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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…

Q: Find the absolute extremd of the on the closed interval. 6x2 g(x) (-2, 1) X - 2 minimum (x, y)…

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Q: Let g(x, y) = 3x²y + y³ - 27y

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Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

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Q: Find the absolute minimum and absolute maximum of f(x, y) = 13 – 8x + 10y on the closed triangular…

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Q: Express y = 3x2 – 8x - 1 in the form y = 3(x – p)² + q, where p and q are constants and hence find…

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Q: Find the maximum value that f(x, y, z) = x² + 8y - z² can have on the line of intersection of the…

A: Given function is f(x,y,z)=x2+8y-z2 and the other constraints are g(x,y,z)=2x-yh(x,y,z)=y+3z We…

Q: Find the minimum and maximum values of: f (x, y) = x² + xy bounded by the graphs y = x´ and y =9

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: on the closed triangular region with vertices (0, 0), (9, 0) and (9, 11). List the minimum/maximum…

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Q: Find all critical points of f(x, y) = x3 + 3x2 −9x+y3 −12y. Classify each one as local maximum,…

A: For extreme values we put fx and fy=0 and solve it.

Q: Consider the function f(x, y) = y6 - 3x²y + 3x² Compute the stationary points of the function f(x,…

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Q: Find the minimum and maximum distances between the sphere r²+y²+z² = 9 and the point (2, 3, 4).…

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Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: Determine the global extreme values of the function on the given domain. f(x, y) = 7x2 + 5y2, osxs…

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Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

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Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: Find the absolute minimum and absolute maximum of Remaining time: f(x, y) = 18 – 8x+9y on the closed…

A: Given f(x,y)=18-8x+9y ∴fx=-8, fy=9 (-8,9) is a critical point Given Region is triangle with vertices…

Q: Find the absolute maximum and absolute minimum valu nty=t-Vt, [-1, 5]

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Q: Find the absolute maximum and minimum of the function f(x,y) = 2y + 64x – 14 over the closed region…

A: The solution is given in the next steps.

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: Find the local minimum xalue of f(x.y)= yds xy

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Q: Find the absolute maximum and minimum values of f on the triangle with vertices (0,0), (3,0), and…

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Q: Find the point on the line y = x that is closest to the point  (3, 1).[Hint: Express the distance d…

A: Assume d be the distance from point y=x to the line y=x Assume (x,y) be a point on a line ⇒(x,y)…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

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Q: Find the maximum value of z=140-x+3y, under the consentrate; x≥0, y ≥0, and  2x+y ≤10, 2x+4y≤28 BE…

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Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…