а) If x, y and z are independent variables and f(x, y, =) =xsin( y + 3:) then find . b) Find all points of local maxima and local minima of the function f(x) = x² - 3x+3.

Q: 5. Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

A: Answer

Q: Find the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1)

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Q: Find a point a* that satisfies FONC (Vƒ(x*) = 0) for f. Then determine if this point is a local…

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Q: Find the relative maximum and minimum values. [6.3] 23. f(х, у) 3 х3 - бху + у2 + бх + Зу - } 24.…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 5 Let glx, ,x -x + 16x, -4x3 . Firid the stationary points and detesmie if t is a maximm saddle…

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Q: Consider the function f(x, y) = 2x²y²-y4 - 8x² Compute the stationary points of the function f(x, y)…

A: Let us consider the given function f(x,y) To find the maxima and  minima Find the partial…

Q: Find the extreme values of f(x, y) = x² + 2y² subject to xy = 4 using Lagrange multiplier method.…

A: Here we have to use the Lagrange multiper method

Q: # 13) Find two positive numbers x and y for which 2x +y = 30 such that xy² is maximized.

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Q: Find constants a and b so that the minimum for the parabola f(x) = x- + ax + bis at the point (5,…

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Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

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: Find all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

Q: (b) Find the global maximum and minimum values and indicate where they occur. f (x) ,x, ) = 2x, + x,…

A: Find the global maximum and minimum values and indicate where they…

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

Q: 1. Find all absolute maxima/minima and saddle points of f(x, y) triangular plate bounded by the…

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Q: Suppose that the quadrature formula has degree of accuracy atleast 2 integral f(x)dx with upper…

A: Given: The degree of accuracy of the quadrature formula is at least 2, and ∫−22fxdx=a1f−2+a2f0+a3f2…

Q: 7  please answer, type the solution if you can please. or write clearly

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

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Q: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

A: Due to Bartleby guidelines, only 1st question can be answered if multiple questions have been asked.…

Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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Q: 9. Determine all of the local minimum points, local maximum points, and saddle points for the…

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

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Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: ) Find the maxima and the minima of z=f(x,y) under the condition y=2x. (d) Find the maxima and the…

A: Max or  Min f(x,y)=(3x2+5y2)e-x2-y2subject to    y=2x

Q: 8. Find the local minimum and the local maximum and saddle points of f (x, y)= x² + y' - 3x² - 3 y²…

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Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

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: Maximize F=x+y subject to:  x+2y≤8  x≤6  x, y ≥0 Corner points at ____________________ Maximum…

A: We have to find maximum.

Q: Find the minimum values of the function (x, y) = x² + 2y² that lic on the cirele x² + y² =1

A: Given : Function fx,y = x2 + 2y2  Circle x2 + y2 = 1   To find : Minimum values of the given…

Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

A:

Q: Determine the values of constants a, b, c, and d so that f(x) = ax + bx + cx +d has a local maximum…

A: We have to determine the value of a, b, c and d

Q: Consider (x, y, z) = x² + y² + z² + 2xyz. Show that (0,0,0) and (-1, 1, 1) are both critical points.…

A: Here we solve the given calculus problem.

Q: 3. Find the Absolute Minimum and Absolute Maximum of f(x,y)=xy subject to 2x² +8y² =144 Fully…

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Q: Find all points (x,y) where f(x.y) has a possible relative maximum or minimum. f(x.y) = x* - 32xy +…

A: Solution:Given thatfx,y=x4 -32xy+8y2-10we have to find all points x,y where fx,y has a possible…

Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

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Q: The absolute minimum of f(x) =x² – 4x On [0,3] is y= %3D 540 .BO -4 .CO -3

A: We use first derivative test to find absolute minimum.

Q: Find the extreme values of f(x, y) = x² + y² subject to the condition x²y = 1 using Lagrange…

A: solution is given below..

Q: A linear function ƒ (x, y) = ax + by + c has no critical points. Therefore, the global minimum and…

A: For the solution follow the next step.

Q: Find the maximum and minimum values of the function f(z, g) ry subject to 3z+ 2y = 18 Maximum value:…

A: Given : f(x, y) = x²y subject to 3x² + 2y² = 18

Q: Determine a minimum of f(x) = x² + 3x², Starting from x, = (6,3) = 6i + 3j and applying the method…

A: The given function is fx=x12+3x22 . The initial point is x0=6, 3. Let it be X0=6, 3. The gradient of…

Q: Find the minimum and maximum of 1 on the interval [0, 3].

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Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: maximize f(x,y)=xy subject to the contraint 6x+y=18  the last question is what is the maximum valye…

A: max . fx,y=xyS.t 6x+y = 18     6x+y=18⇒ 6x+y-18=0∴ gx,y=6x+y-18=0    Fx,y,L=fx,y-L g x,y⇒…

Q: Consider (r, y, z) = x² + y? + 2? + 2ryz. Show that (0,0,0) and (-1, 1, 1) are both critical points.…

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Q: -- ) Determine the values of constanas a, b, c, and d so that f(x) = ax³ + bx² + cx+d has a local…

A: As given (0, 0) is a point of local maximum and (1,−1) is a point of local minimum of f(x). The…

Q: 5. Assume that the following conditions exist fi = 0 2= 0 Does a maximum, minimum, or saddle point…

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Q: find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. kx2…

A: The given family of curves is kx2+y2=1. Differentiate both sides of the above equation with respect…

Q: Let fx) = x + 2x-8. For what value(s) of x does fx) have a local minimum?

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.