Identify the removable discontinuity. f(x) =  x3 + 2x2  over  x + 2

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: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: To find the critical points we solve dy/dx=0

Q: The total daily profit (in thousands of pesos) of a certain food company for the sale of x boxes of…

A: Given query is to find the number of box needs to be produced to maximize the profit.

Q: 11. Differentiate the function (use chain rule): y = x²(x-1)³(2x-5)² ;

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Q: The absolute minimum of f(r) = 20z² – I+1 is

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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: Q3/ Optimize the function Z = x + xị ? Subject to: x1 + x2 = 4 x1, x2, 20 Using Lagrange…

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Q: Find all points (x.y) where f(x.y) may have a maximum or minimum. f(x,y) = - 3x + 5xy- 2y² +x+y

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Q: find the extrema (minimum and maximum) of f(x) = x2-1 on (-1,2). If none, explain why.

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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: (f) What is the first-order condition implied by unconstrained maximization of I1 X 1333 X, where x…

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Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given that,

Q: The function y = 2x2 - ln 4x (x 7 0) has one minimum point. Find its first coordinate.

A: Given  y = 2x2 - ln 4x

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

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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: Show that the function f(x,y) = x³ + y³ – 63(x +y) + 12xy is maximum at (–7,–7) and minimum at…

A: Given function: fx,y=x3+y3-63x+y+12xy Formula Used: D-Test: For each point a,b where fxa,b=0 ,…

Q: Find the absolute maximum and minimum of the function f (x , y) =x² + y² on a closed triangular…

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Q: Find the maximum and minimum values of the functions f(x, y) = 4x + 4y-x -y subject to the condition…

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Q: Find and classify the critical points of the function f (x, y) = 16x³ – 12x2 + 12xy? + 3y?

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Q: The population density of a city is given by P(x,y) = - 25x - 30y + 500x + 240y + 180, where x and y…

A: Population density is given by following function  P(x, y) = - 25x2 - 30y2 +500x + 240y + 180

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

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Q: he population density of a city is given by P(x,y)= -20x²-20y +440x + 280y+200, where x and y are…

A: solution is given below

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

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

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Q: Maximize f=-x-3y subject to -2x+y = 2 X,y >= 0

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Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

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: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: . Determine the values of constants a and b so that f(x) = ax² + bx has an absolute maximum at the…

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Q: Find the absolute minimum and absolute maximum for y = x3 – -+ 4x +1 on [-2,2].

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Q: Determine the maximum number of turning points of f. 6. f(x) = (x – 2)2(x + 4)2 7. Identify the end…

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Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval (0, 4]|

A: The absolute vale in the interval [0,4] for f(x) will be either at critical points or at end points.

Q: Consider the function f(x)=xe^-7x, 0≤x≤2. Find The absoulute mininum and maximum.

A: Given data: The given function is f(x)=xe-7x. The given limits of x are [a, b]=[0, 2]. The first…

Q: Show solution/process. 1. f(x) = 2x² – 4x + 5 at the point (–1,11) 2. f(x) = v25 – x² at the point…

A: Since there are more than one question, only one question can be answered. The function is given by,…

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

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Q: Calculate the difference d between the global maximum and global minimum values of f(x)=x2−4x+6 in…

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Q: 1 - X 0 3

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Q: Determine all the critical points for the function y = Vx² (2t- 1)

A: Given function is in two variables x and t For critical points we calculate Partial derivatives…

Q: find the critical point and classify the function f(x,y) =xlny +x2 -4x-5y+8

A: Answer

Q: For the function f (x) =x³ – 3 -x² + 8 , find the coordinates of all Critical Points.

A: Given, fx=x3-3x2+8

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

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Q: f(x) = -x + 6x + 5 on [5, 8] %3D maximum minimum

A: Differentiate wrt x and put derivative to zero for maxima and minima  If value of x lies on given…

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: B3(a): Find the critical points of the function f(x) = 6x² – 12x. %3D

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: 4) Where is the function g(x) = 3x2 -x+ 5 differentiable?

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Q: The population density of a city is given by P(x,y) = - 20x - 20y + 560x + 440y + 200, where x and y…

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Q: Find the minimum and maximum of x3+3x². on the interval [0, 3].

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

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