1. Find the minimum and maximum values of the expression where r and y are the lengths in Figure 1 and 0 10 X10-a (c) a+2y (a) x (d) 2x+ (b) y a 10 5

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A: To find the minimum value of the function f(x,y)=(x-1)2+(y-1)2 subject to constraint x2+y2=8. Let,…

Q: 8. What is the minimum value of the function defined by y = cosx + 4? В. З A. 2 C. 4 D. 5

A: Given- y=cosx+4 To find- The minimum value of the expression.

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A:

Q: Determine two positive numbers e and f whose product is 27 and for which the value of 4f +3e is a…

A: Product is 27 and 4f+3e is a minimum.

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Q: The relative minimum of y= x² – 4x+4 occurs at A x = -4 B) x = 4 c) x= -2 D None of the given…

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Q: 10. Given that f is a quadratic function with minimum f(3) = 6, find the vertex, range, and…

A: Consider the given question,Quadratic equation is a parabolic equation and its vertex is highest or…

Q: The relative minimum of y= x - 4x +4 occurs at A None of the given choices B) x = -2 c) x = -4 D) x…

A: We can find the relative minima or maxima by finding x where the first derivative vanishes (critical…

Q: 8. What is the minimum point of the given function y = x² – 6x + 10? B. k = -3 A. k = -1 C. k = 1 D.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that x and y are two positive numbers, and suppose that r+ 2y = 30. Find the maximum value…

A: Given that: x+2y=30…

Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum.

A: To solve the following problem

Q: 1. (a) Find the maximum value of f(x, y, z) = 16x + 2y + 4z, subject to the constraint x² + y+ z² =…

A: Introduction: When we extremize a multivariable function under certain constraints, we use the…

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Q: Find the absolute minimum value of the function f (x, y) = 2x² + 2y? subject to the constraint 9x2 +…

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

A: We need to find the local minimum value of f(x,y)=4+x7+y7-7xy.  For this we find the partial…

Q: Suppose two numbers x, y satisfy x – y = 4. The minimum value of the quantity x² + 3y? is O 24 12 36

A: Given  x-y =4 Then x=y+4 And minimum value of u=x2+ 3y2   ...(1)

Q: On a cosine function y=Acos(Bx)+C, which of the following expressions will always calculate the…

A: The cosine function is  y=Acos(Bx)+C

Q: 16. Let h(x, y) = xy – 2x². Find the minimum and maximum values of h on the rectangle where 0 < x <…

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Q: 1. The vertex of y = −(x+1)² +4 is a maximum. -2. The function y = (x+1)² in standard from is…

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Q: Determine the maximum r-values of r = 7cos4e. e= 0, 2 4 4 e= 0, T, 2 2 e= 2 e= 0,. 4' 4

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Q: Suppose f, f', g, and g' have the following values: 1 2 3 f(x) 4 - 2 - 2 7 4 f'(x) 9 2 5 - 9 (x)6…

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Q: The graph of  f(x) = 2(x − 2)2 − 7 is a parabola that opens upwards with its vertex at (x, y) = 2,−7…

A: Consider the graph of f(x) = 2(x − 2)2 – 7

Q: The minimum value of the function f(z, y) = (z- 1)2 + (y-1)2 subject to the constriant 12 + y = 8…

A: To find the minimum value of function ee use here Lagrange multipliers method

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

A: Legranges multiplier

Q: Given: f(x) = x³ – 6x² − 15x + 7. Find the LOCAL MINIMUM point of f (x). A. (5, ƒ (5)) B. (−1, ƒ…

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Q: 1. Find the maximum value of f(x, y) = 4xy where x > 0 and y > 0, subject to the constraint 9. = 1.

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Q: Suppose that r+ yl + lr - yl = 2. What is the maximum possible value of 2- 6z + y? (A) 5 (B) 6 (C) 7…

A: Consider a equation: x+y+x-y=2……1   and the expression, x2-6x+y2……2

Q: What are the local max and minimum points of y=x^3-3x+1

A: The given function is: y=x3-3x+1

Q: What is the minimum value of the function f(x, y) on the set D = {(x, y) | 16z² + y² < 1}? = e…

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Q: The relative minimum of y= x² – 4x +4 occurs at (A) x= -4 B None of the given choices c) x = -2 D) x…

A: We have to find out

Q: Find the maximum value of 5x2 - 4xy+ 8y subject to x+y? = 1..

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Q: What is the minimum value of f(x, y) =x +4y - 2x +8y subject to the constraint X+2y D7 O a. 5 O b.…

A: Use Lagrange multiplier to solve

Q: if the function f(x)= x^3+ax^2+bx has the local minimum value -2/9 cube root 9 at x= 1/cube root ,…

A: Given fx=x3+ax2+bx has local minimum value -239 at x=13 to find  value of a and b explanation as…

Q: What is the minimum value of the function f (x, y) = e*y on the set D = {(x, y) | 16x? + y² < 1}?…

A: Given function is fx,y=e-xy  on the set D=x,y: 16x2+y2=1

Q: Find the minimum and maximum values of the function f(x, y, z) = 5x + 6y + 4z subject to the…

A: Here we have f(x,y,z)=5x+6y+4z subject to the constraint x2+6y2+6z2=1 Let g(x,y,z)=x2+6y2+6z2-1

Q: If x and y are two positive numbers that satisfy xy = 7, then what is the minimum value of 2 x +3 y…

A: Find the minimum

Q: What is the minimum of the function y = –x° + 3x for x < -1? O 2 O-4 4 O-2

A: We can solve it graphically. Graph of f for x&lt;=-1:

Q: Find the maximum value of z = xy2 subject to 8x2 + y2 = 1944; x > 0, y 2 0. z =

A: Given z=xy2 and condition 8x2+y2=1944; x≥0, y≥0 Let F=xy2+λ8x2+y2-1944 Partially differentiating…

Q: f(x) = x² – 4mx + 6 %3| 7- Since the local minimum value of the function is -30, m = ? (m will be…

A: The given function is; f(x) = x2-4mx+6

Q: 20. Find the minimum value of ry+xz+ yz given that r, y, z are real numbers that satisfies the…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum. a. 1 and 2…

A: we have to find

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: Sketch the following problem graphically: max f X2 = X2 subject to g1 = x1 – (1 – x2)³ < 0 92 = X1 2…

A: Given - Sketch the following problem graphically. maxx2f = x2subject to g1 = x1 - 1 - x23 ≤ 0…

Q: 6. (a) Maximise f (r, y) = 2r + y subject to 2a2 + y = 1 (b) Minimize f(r, y) = 2r + y subject to…

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

A: The function has only one critical point. Therefore it has maximum or minimum.

Q: Suppose the labor cost​ (in dollars) for manufacturing a camera can be approximated by…

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Q: Find the minimum and maximum values of the function f(x, y, z) = 3x + 2y + 6z subject to the…

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