Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y = 3x + 2. Show that f is a quadratic function, and find its minimum value by completing the square.

Q: Find the maximum and minimum value of f(x,y) =x3+3xy2-3x2-3y2+4

A: fx,y=x3+3xy2-3x2-3y2+4   fx=3x2+3y2-6x   fxx=6x-6   fxy=6y   fy=6xy-6y   fyy=6x-6

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

A: Given

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

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Q: Find the maximum value of xy if it is required that 2x + 7y = 35 %3D

A: Given  2x+7y = 35  y=(35-2x)/7 Let M = xy  To maximize the value of xy=M we need to differentiate…

Q: Suppose that f(x, y) = 4x* + 4y* – xy Then the minimum is

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Q: Find the local maximum and local minimum in (x,y) notation for the following: y=(2x2-7x)/(2x+5)

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Q: Suppose that f(æ, y) = e-3x² – 4y? + y Then the maximum is

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Q: Find the local minimum value of f(x, y) = 4 + x° + y° – 9xy. ::

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Q: Find the absolute maximum and absolute minimum of the function f(z) = z² – 6z + 5 over (1,

A: Given: fx=x2-6x+5, 1,6

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: You will calculate L5 and U5 for the quadratic function y 2² + z + 14 between z = 0 and z = 2. Enter…

A: To solve the following problem

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

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Q: Suppose that f(x, y) = 3xª + 3yª – 2xy Then the minimum is

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Q: Suppose that f(x, y) = 3x* + 3yª – 2ry Then the minimum is

A: Given, f(x,y)=3x4+3y4-2xy

Q: Find the local minimum value of f(r, y) = 4 + x7 + y7 – 7ry.

A: We have to find the local minimum of the function f(x,y).

Q: The function f(x,y) = 3x2 - 2xy + y2 + 8y has one stationary point. What is the location and…

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Q: Find the absolute maximum and minimum of the function on the given domain. f(x.y) = 6x + 5y on the…

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Q: Suppose that f(x, y) 3x + 3y* 2xy Then the minimum value of f is

A: We have to solve given problem:

Q: Consider the function f(x) = - 2x + 24x2 42x +4. %3D - Find the critical points.

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Q: Find the maximum value of f(x,y) = 25 - x - y on the line x+ 4y = 17. %3D

A: First-order derivative test for Maximum value : - The slope of a function is determined by its first…

Q: Find the local minimum value of f(x, y) = 4+ x³ + y³ – 5xy.

A: Explanation of the answer is as follows

Q: The position function of a particle is given by 7(t) = (t², 5t, t2 – 16t). When is th sneed a…

A: Given:

Q: Find the maximum and minimum values of the function y 32t-t on the Interval [4, 61. %3D maximum…

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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: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

A: The points where the tangents are horizontal are the points at which slope is zero.That means,…

Q: Find the local minimum value of f(x, y) = 4 + x15 + y!5 – 15xy.

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Q: Consider the function f(x,y) - x-44x- 4y and determine if, at the point (4,0) if the function is a…

A: Note: Since you asked multiple questions I solved one. For solution of other problem please post the…

Q: Find the maximum of the function f(x, y) = 4xy – x² + 2y² subject to the constraint a + y = 1. Value…

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Q: Find the maximum value of ƒ(x, y) = 49 - x2 - y2 on the line x + 3y = 10.

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Q: Find the absolute maximum and minimum values of the function on the triangular region whose vertices…

A: The given function f(x, y) is a polynomial and therefore, it is continuous and has both maximum and…

Q: | Find the minimum point for the function f(x) =1 + 12x – 4x (2,-7) (0, 1) Oa.9) (1, 9) O (-1, -7)

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Q: Find the minimum value ofx +y +z² given x+y+z=3a.

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Q: Use the method of Lagrange multiplier to find the absolute maximum and absolute minimum values of…

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Q: Find three positive numbers x, y, and z whose sum is 21 and product is a maximum.

A: There are two different questions in the image. According to our guidelines, we can solve only one…

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x + 3y = 10.

A: Solution of given question is written in below steps.

Q: Find the absolute meximum and absolul-e minimum of fcx) = X intereval [4,8] x- 48X Over the

A: From the given function; fx=x33+x2-48x First, we have to find the critical points; As we know that,…

Q: Find the local minimum value of f(r, y) = 4+ a7 + y7 - 7ry.

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Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

A:

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: Suppose that f(x, y) = e e-x² - 2y² + x Then the maximum value of f is

A:

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

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 absolute maximum value and absolute minimum value of f(x, y) = 2a2 + 2y² + 4y – 1 on the…

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Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…

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

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Q: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

A: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

Q: If x² + y² < z < 1, find the maximum and minimum of the function u(x, y, z) = x + y + z

A: We have to find the maximum and minimum of the function.