Q7:- Find the extreme value of the function f(x,y) = 4xy - x - y*. Q8:- Find the extreme value of the function f(x, y) = x3 + y3 - 3x – 12y + 20.

Q: Find the values of æ, y and z that correspond to the critical point of the function z = f(x, y) =…

A: We need to find values of x , y , z.

Q: Find the critical numbers of the function

A: We find g'(y) using the quotient rule

Q: The function f (x, y) = 3x3+y2-9x+4y is given. a) Find the critical points of function f. b)Do…

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Q: Find and classify the critical points of f(x,y) = 2 – x +2a2 - y². %3D

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Q: The cubic function y = ax3 + bx² + cx + d pass through (0, -6), (1, -2) and tangent to the line 3x –…

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Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

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Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x? +…

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Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 2x?.…

A: The given function is  f(x, y) = 2x2 - 5x - 3y + 5y2 To find the critical points of the function.

Q: Maximize Q = xy, where x and y are positive numbers such that x+3y 16. The maximum value of Q is and…

A: Maximize Q=xy, where x and y are positive numbers such that x+3y2=16

Q: Q2:- Find the maximum value of the function f(x,y) 49-x-y? on the line x+ 3y = 10. %3D

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Q: The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use the…

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Q: Find all the critical points of the function 1 3 f(x,y) = x° -6y-7x+18y-3 What are the critical…

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Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 2a? –…

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Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x? –…

A: Given function is fx,y=4x2−7x−6y+2y2 Differentiate fx,y=4x2−7x−6y+2y2 partially with respect to x…

Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: Examine the function (x, y) = 5x-+ 2xy+ ɔy²+ 96x+ 288y for relative extrema. (-4, –28) (-4, –28) a.…

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Q: Q4. Find the maximum and minimum value of fusing Graphical method, where f= 25x, -16x, subjected to:…

A: Consider the given function. f=25x1-16x2 And the subject is defined as,…

Q: Q4: Find and classify all critical points for the function: z2 = (x3/3)-(y3/3)+2xy

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Q: Find the minimum and maximum of the function y = z° - 3125z on [-7,7] by comparing values at the…

A: The function is given as , y=z5-3125z over interval -7,7 find maximum and minimum of the function.

Q: 2. Find an equation and sketch the graph of the level curve of the function f (x, y) = 16 – x² - y2…

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Q: 2. Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³. %3D (1

A: Given: 2.Let us consider the given curve equation, fx,y=7x-8y+2xy-x2+y3 -----1

Q: . Find and classify all the critical points of f (x, y) = 7x – 8y + 2xy – x² + y³.

A: (2)  Given data curve is  f(x,y)=7x-8y+2xy-x2+y3.............(1) then fx=7+2y-2x    &amp;…

Q: Find the critical point and determine if the function is increasing or decreasing on the given…

A: Please refer the attached image for complete solution.

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: f(x) =4 on the interval (-1, 4)] Find the critical points of the function

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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: Find all the critical points for the function f(x, y) = x² + 8xy + 4y² +3. (Use symbolic notation…

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Q: Q2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

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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 all points (x,y) where f(x,y) has a possible relative maximum or minimum. f(x,y) = x4 - 4xy +…

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Q: Find the critical points of y= 2x^3 +3x^2–12x and apply the Second Derivative Test to find the…

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Q: Q2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

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Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

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Q: Find the critical numbers of the function. y - 3 y2 – y + 3 g(y) = y = 0 (smaller value) y = 3 |×…

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Q: 3.Find the coordinates of the points on the curves y =x3 -3x2-12x+10 with the gradients -2.

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Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 3x? -…

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Q: Find the absolute maximum and minimum of the function f(x,y) = 2x - 8x + y - 8y + 2 on the closed…

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Q: Classify the critical point (5,-4) for f(x,y) = x² + 4xy + 2y2 + 6x-4y +3

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Q: (b) Find the linearization of function S(x) = Vx V220 at a=216 and use approximate number (c)Find…

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Q: On the graph of f(x)=cosx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: We know,  -1≤cos x≤1 for any real value of x.

Q: Find the minimum and maximum of the function y = z – 1280z on [-5, 5] by comparing values at the…

A: The given function is

Q: Find and classify the critical points of the function f(x, y) = x³ – 10.5æ? – y? + 5 - -

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Q: 2. Integrate the function (x+2/x)ax using multiple-application trapezoidal rule with n= 3

A: Trapezoidal Rule: ∫abf(x) dx≈∆x2(f(x0)+2f(x1)+ ... +2f(xn-1)+2f(xn))where ∆x=b-an

Q: Find the critical point of the function f(r, y) = – 4+ 8z + 7z - 5y + 6y

A: Find the critical point (x,y)

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) 4x? – 4x…

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Q: Find the critical points of the function f (z) = 25z 3 + Enter your answers in increasing order. If…

A: fx=25x23+x53 To find: The critical points of f(x).

Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

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Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

A: According to mean value theorem,Let f be continuous on [a,b] anddifferentiable on (a,b). Then…

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.