Question 3. Let f(x, y) = x³ + y³ – 3xy. Determine all local minima, maxima and saddle points of f.

Q: Question 2 a. I b. | function f(x, y) = y² − x² + — a 1 Find the critical points of the function…

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Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

Q: Q#5. Locate all relative extrema and saddle points of 4 4 f(x, y) = 4xy - x' - y' as shown in figure…

A: We have to solve given problem:

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

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Q: 4. Let A(x) = ſ dt. Find the local minima, local maxima, and t2+1 inflection points of A(x).

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Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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Q: ) Find any relative(local) extrema and saddle points of f(x,y)=xª+yª-4xy+1.

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Q: g(x) = x + 2 (2, 4) (blue line) f(x) = x² (black curve) A (-1, 1) 1-

A: From the given bounded region; Now use the double integration method to find the area between the…

Q: Locate all relative extrema and saddle points of f(x,y) = 4xy – x* – yª as shown in figure below 0…

A: First, we need to find all critical points,…

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval: y = ex − x,…

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Q: Question 1 Find and classify the critical points of the function f(x, y) = y* – 2y² – x³ + 3x.

A: The given function is: f(x,y)=y4-2y2-x3+3x

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 5y sin (3x)

A: Using second derivative test :Let the partial derivative of f be continuous on a disk with the…

Q: Step 3 of 5 In order to maximize V(x), we need to find the critical points of V(x). Find the…

A: To find the derivative of V(x)

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

Q: QUESTION 10 Let f (x, y) be a function and fxx = 2xy, D(x, y) fx fyy -fxy fxy x2- 3y. Then what is…

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Q: 7  please answer, type the solution if you can please. or write clearly

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Q: Find all Max., Min., Saddle point for the functions below: P(x) = 2xy-5x²-29² + 4x +49-4

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Q: The nature of the stationary point (0, -1) for the function f(x,y), if f= 4-12x, fy= 0 and fry=-4+…

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Q: 10. Find the local maximum and minimum values and saddle point(s) of the function f(x, y) = x3 –…

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Q: Let f (x, y) = 1 + 3? – cos(2y). Find all critical points subject to y E [0, 27]and classify them as…

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Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: 7

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Q: VI. Determine all the relative minimum and maximum values, and saddle point/s (if any) of the…

A: Given,  h(x,y)=x3-3x+3xy2

Q: Locate all relative extrema and saddle points of f(x,y) = 4xy - x*-y* as shown in figure below 0-1-2…

A: The Second Derivative Test for Functions of Two Variables If D>0 and f_xx(x_c,y_c)<0, then…

Q: 4. Find the local maximum, minimum and saddle points for the function f(x, y) = 6x? 2a3 + 3y? + 6xy.

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 6y sin (2x)

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Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² - 2x³ + 3y² + 6xy. b. s]…

A: Extreme Points of Function f(x,y)=6x2-2x3+3y2+6xy

Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² − 2x³ + 3y² + 6xy. b. s]…

A: Given :fx,y=6x2-2x3+3y2+6xy

Q: 6 Find all Max., Min., saddle point for the functions below: 3 f(x,y) = x ²³ + 3xy ² - 15 x +…

A: Given: f(x,y) = x3+3xy2-15x+y3-15y

Q: 3. Find the fixed point(s) of f: [1, ∞)→→ [2, ∞) defined by f(x) = √²+x.

A: 3) To find: fixed points of f:[1,∞)→[2,∞) defined as f(x)=x2+x.

Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

Q: f(x, y) = ln(108x +9y) + 6x² - 9y Local maxima are none Local minima are none Saddle points are none…

A: Given f(x,y)=ln(108x+9y)+6x2-9y

Q: 1. Find any local maximum and minimum values and saddle point (s) of the function f(x, y) = -6xy +…

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Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: Q2.Find all the local maxima, local minima and saddle points of the function f(x, y) = In(x + y) +…

A: Using the rule of saddle point on f(x,y).

Q: Find out all the relative minimum and maximum values, and sadle points of the function h defined by…

A: Here we have h(x,y)=x3-3x+3xy2 .............................................. (1)

Q: Question 12 Find the linear approximation of the function f (x, y) = 2x – y + a²y - near the point…

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Q: Find all the local maxima, local minima, and saddle points of thefunctions ƒ(x, y) = ey - yex

A: Given: fx,y=ey-yex

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) =x° - 3xy + y

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 5. Find the local extreme values of f(x, y) = x²y on the line a +y = 3.

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Q: 9. An equation of the line normal to the graph of f(x)=, at (1,–1) is (a) 2x - y -3 -0 (b) 2x + y…

A: Explanation: Given that  f(x)=xx-2 at (1,-1)   Concept Used: To find the normal firstly find the…

Q: In this problem we will find and investigate all local maxima, local minim. and saddle points of the…

A: Given fx,y=x4+y4-4xy2-xy+2x Taking first partial derivatives: fx=4x3-4y2-y+2fy=4y3-8xy-x Putting…

Q: Question 4. Find local maximum, local minimum and the saddle points of the given function. f(x, y) =…

A: Given, f(x,y)=2x5-40x2+y2-6y+10To find: Local maximum, Local minimum and Saddle points

Q: Find the highest point, low point and saddle point (if any) of the f(x, y, z)=3x² + 2xy + y²

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Q: EXAMPLE 3 Find the local maximum and minimum values and saddle points of f(x, y) = x4 + yA - 4xy +…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.