O ACTIVITY 2: Sketch the graph of the quadratic function y = x2 - 4x + 3 and determine the direction of the arabola, vertex, axis of symmetry, domain, and range. YCHAL to e ) og to af (6) rb to Direction: as eno amo ot ior bee Vertex: Axis of Symmetry: woled an Domain: sl od slovion3 ei sil foldW Range: ollot od to doiW

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Given:

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Find the extrema of f subject to the stated constraint f(x, y) = 3x + 2y, subject to 2x2 + 3y2…

A: Given:- f(x,y)=3x+2y ........................ (1)  and subject to 2x2+3y2=6…

Q: Let (S) be the part of the sphere (x – 3)² + y² + (z – 1)² = 4 tha Then (S) is the graph of the…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: n F(x, y) = x² + 2y. A

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Q: 4-18 Three points, (xt, J'1), (x2, J'2), and (x3, y3), lie precisely on the straight line Y = a +.…

A: Let (xi, yi) , i=1, 2,3,....n be a given sample of size n And the equation of the straight line be…

Q: Q- fiad theare eaclosed by the given curve 1- The parabola x = —y? and the line y = x + 2 2 The…

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Q: Sketch a graph of I = t + 2t, y = t +2, t > –1 . %3D

A: Given equations are x=t2+2t,y=t+2,t≥-1. So list the values of t and obtain the coordinates in…

Q: The graph below shows contours of f. Does f have a maximum value subject to the constraint g(x, y) =…

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Q: 3. Find the maximum and minimum values of f(x, y) = x² + y² - 2x - 2y + subject to the constraint…

A: We use langrange multiplier method

Q: Let A and Abe the maximum and minimum values, respectively of the function f (x, y) = 4x +y? subject…

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Q: Consider the graph C in the y-plane given by the polynomial p(x), where p(x) = ax? + bx + c, and a,…

A: System of linear equation.

Q: Find maximum and minumum values of f(x, y, z) = 3x – 6y + 15z subject to the constraint x2 + y? + z2…

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Q: B. Find the extremum of f(x, y) = -x - y subject to the constraint y + 4.x = 1. Use a graph of the…

A: We will answer the first question since we answer only one question at a time. Please resubmit the…

Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

Q: 3) Sketch the graph For the Following Functiones. a) 2: 3-2x-6y b) Plane 23+Z =H H

A: We shall give graph of the 3d diagrams in next steps. We shall sketch for first 3 subparts only.

Q: (d) | (3+ecos (0 sd AX ·

A: As per your query the solution of the problem (a) has been done in midpoint rule. For the solution…

Q: 2. Show that ( 1, 6), (0, 3), (1, 2), and (2, 3) lie on a common parabola.Hint: For scratch work,…

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Q: Review later 7. Explain the difference in the movement of the parent function, f(x), given the…

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Q: b) y = 2 – 5sin (3x) Q3) Use shifting graph to sketch a) y = |Vx – 4|– 2 b) y = 2+ 3cos (2x)

A: 3)Given isa) y=x-4-2fx=xfx-4=x-4fx-4=x-4y=fx-4-2y=x-4-2b)let fx=cos xf2x=cos 2x3f2x=3 cos2x2+3…

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x² + y? +…

A: Hair we use langraj multi plier method to solve the the given problem.

Q: Find maximum and minumum values of f(x, y, z) = 6x – 12y + 30z subject to the constraint x2 + y? +…

A: We will use the Lagrange's multiplier to to find the minimum and maximum of the solution when the…

Q: 1. Sketch the graph of the domain of the function f (x, y)= sq x / x−y​ 2. Compute the equation of…

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Q: phically. (use graphing paper 2x +3y 9 2. 16x + 9y = 27 %3D %3D Y substitution method.

A: We have to find the solution of equation

Q: Show that (−1, 6), (0, 3), (1, 2), and (2, 3) lie on a common parabola.Hint: For scratch work, plug…

A: Consider the three points (−1, 6), (0, 3) and (1, 2). Substitute the above three points in the…

Q: Q Use Lagrange multipliers to tind the maximum an Ċ minimnm valnes and Points (x ) at which they…

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Q: Sketch the graph for c=0 and then explain how the graphs (level curves or surfaces) change for the…

A: Given f(x, y, z)=x2-y+z2 To find the graph we need to find level surface of equation, equate the…

Q: Find maximum and minumum values of f(x, y, z) = 5x – 10y + 25z subject to the constraint æ? + y² +…

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Q: Date: Section %3D Practise: The Quadratic Relation y = ax + c 8.3 1. Without graphing, order the…

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Q: Find a constrained minimum or maximum of the function f(x, y) = xy subject to the constraint 4x? +y²…

A: Consider gx,y=4x2+y2 and evaluate the partial derivatives of fx,y and gx,y with respect to x and y.…

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: C. Find the extrema of f(r, y) = x? + y subject to r² - y? = 1. Use a graph of the contours and…

A: Given function is f(x,y)=x2+y subject to  ϕ(x, y)=x2-y2-1      (*)

Q: Maxmize f(x,y,z) =x2y2z2 subject to the constraint 2x2+4y2+6z2=10. assume x,y,z are positive  when…

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Q: b) find the coordinates of any stationary points for the eurve of f(xx) and determine their nature.…

A: Given- fx=-x33+3x24+9x2 To Find- (a) The stationary point of the curve.                (b) Intercept…

Q: nath A = 30, B = 20, C = 11, D = 22. 3. Discuss how to evaluate Z enclosing the origin. dz, where C…

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Q: 5) s how that the line af intersection f the Planes and 5x-2y-Z=0 is Paraliel toG Pheline X+23-22= 5…

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Q: Let (m, n)be the point at which a line is tangent to the ellipse + m = 1lf this line has x-intercept…

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Q: The maximum value of the function f(x,y) = (xy) subject to the constraint %3D g(x,y) = + y? = 1, is…

A: Consider the given equation. fx,y=xy6x24+y2=1 Now, apply the Langrenges multiplier. Find the…

Q: For what values of a and b is the line 2x + y = b tangent to the parabola y = ax when x = 1. a = 1…

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Q: Let F(x, y) = (x + 1)j, and let C be the portion of the parabola y = x² that starts at (0,0) and…

A: The integral ∫CF⇀.dr⇀ is positive. From the graph the angle between direction of F⇀ and dr⇀  is…

Q: C. Find the extrema of f(x, y) = x2 +y subject to x2 – y? = 1. Use a graph of the contours and…

A: Given:f(x,y)=x2+y   subject to x2-y2=1

Q: a.Find the maximum value of w = xyz on the line of intersection of the two planes x + y + z = 40 and…

A: Given Data The equation is w=xyz. The first equation of plane is x + y + z = 40. The second equation…

Q: Find the shortest Distance d faumthe point to the plane X+y+Z=8.

A: Let's find.

Q: b) find the coordinates of any stationaly points for thhe eurve of f(x) ana determine their nature.…

A: Given : function fx = -x33 + 3x24 +9x2 To find : (b) Coordinates of stationary points for f(x) and…

Q: The quadratic function f and AMPQ are graphed in the standard (x.y) coordinate plane below. Points…

A: Area of a triangle is 12× base ×height

Q: A student is graphing the function y= Vz+4 on the coordinatė plane. Which statement will help the…

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Q: Describe geometrically all points P(x, y, z) that satisfy the given condition. X = 1

A: Given the points P(x,y,z) that satisfy the condition x=1.