3. Find the location and values for any global extrema of the function 1 f(x) = ³ – 2x° +5 %3D on the given intervals. Show all work and justify your answer. (a) [–1,5]

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A:

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A:

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Q: 1 Q9: Let f(x) = cosx x + 3 then find all critical points. 2 -

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Q: 1) 3 Find the orthogonal trajectories of the family of curves y = 2x+k

A: Please see the explanation below

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A: Given the graph representing the area

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A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

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A:

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

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A:

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

A: Given: For any function y=f(x) can be expressed as x=f(y) in standardmathematical methods for…

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Q: 11. Find the linear approximation of f(x) = √√x_ at a = 1. Use the linearization to estimate the…

A:

Q: Q2:A- Use Rungo value problem: ý=1+², 1≤x≤2, y(1) = 2 with h = 0.2. olynomial approximation (of…

A: Ju

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A:

Q: b) If y(t) is the solution satisfying the initial condition y(0) 1, find the value of lim y(t).

A:

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

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A:

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

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A:

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

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A:

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A:

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: (b) Evaluate (e) Given the function Rx) (x-2 + (y-3) O Find the critical points. (1)

A: The details calculation is given below

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A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

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A: Inverse Laplace transferom

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A:

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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-…

A:

Q: 8. DETAILS SCALCET9M 3.10.003. Find the linearization L(x) of the function at a. Rx) = Vx, a = 64…

A: given,

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A: we need to find the critical value when α = 0.1 degree of freedom is 18 and it is a 2 tailed t test…

Q: 1.4 Using the graph in Figure 1.7 below, find SLaf (t)dt and if the area of the shaded region is A,…

A:

Q: 3. The temperature on a portion of the surface of a metal plate is given by T(x, y) = 4 x² + 2y3 +…

A:

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A: We need to solve this problem using Euler's Method.

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A:

Q: F.M: 15 1. Use second derivative test to classify each of the given critical numbers as a relative…

A: 1. A) f(x) = e-x(x² - 3x + 1)  So, f'(x) = e-x(2x - 3) - e-x(x² - 3x + 1) So, f'(x) = e-x(2x - 3 -…

Q: Find the value of k that makes function continuous at z=4 |2z + 6 z> 4 5z – k z< 4 f(z) = ualuo…

A: Continuity.

Q: QUESTION 7 f(x) = 3 x4-4 x3 -12 x2 +1, has local minimum at x= %3D O A O B 2- ODO

A:

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.