3- Show that the function y = x3 + 3x + 3 satisfy the y" + xy" 2y 0

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: 1 If y = V1-x then y' = 2/1-x

A:

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

A:

Q: 21) Find the maximum and/or minimum values of f (x, y) = x² + 2xy + 2y² - 6y + 2

A:

Q: b) Find the absolute maximum and minimum values of function f(x) = (x– 2)5 over the interval [-3, 4]

A: Absolute extrema can occur either at the points of local extrema or the boundaries of the interval.…

Q: # 13) Find two positive numbers x and y for which 2x +y = 30 such that xy² is maximized.

A:

Q: a) Find all four critical points for the function f(x, y) = y³ + x²y + 9y² + 2x².

A:

Q: + 3 satisfies (1– x² )y"-2 xy'+20 y = 0.

A:

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: ind and classify all critical points of the function f(x,y) = 3x²y + y³ – 3x² – 3y² + 2.

A: We have to find and classify the critical point of f(x,y).

Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

A:

Q: 1. x² = y + 4 and the x – axis from x = - 1 and x = 3.

A: The given problem is to find the area of surface bounded between the given curves. Given curves…

Q: . Show that y x2 2 (xyz)(x – y)(y – z)(z - x) N N

A:

Q: -x-1 a) y' = +2yi-1 v(0)=1

A:

Q: + iv is analyt: and satisfies the a real constant

A: Since f is analytic in S, it satisfies Cauchy-Riemann equations. Thus,

Q: 2 Find the points of intersection öf with equations: 1 a y=-x-7 and y = -5x+ 10 b y-1=-(x – 4) and y…

A: We have to find the point of intersection of the lines with equations so, for that we will find the…

Q: [x² - y² If f(x,y)=2x-2y m if y = x if y=x then:

A: Given the function,   fx,y=x4-y42x-2yif y≠xmif y=x

Q: 8. Show that y = x° + 3x +1 satisfies y" + xy" – 2y' = 0.

A:

Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

A: Due to Bartleby guidelines, only 1st question can be answered if multiple questions have been asked.…

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: Maximize f(x, y) = 18 - x2 - y2, x + y - 2 = 0.

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Q: Find the maximum and minimum values of the function f(r, y) = x²y subject to 5æ² + 4y² = 60 Maximum…

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Q: I Eliminate the arbitrary constants y = x²+ ax + be*

A:

Q: - Determine the value of y when x = 0-1 given that y(0) = 1 and y =?

A: Given that: y(0)=1 and y'=x2+y

Q: of xy subject to x +y =

A:

Q: 2x +y-z=3 x- y+z=0 y+2z =1. Then x=

A: Given system of linear equations; 2x+y-z= 3 x-y+z = 0    y+2z=1 We can use Cramer's rule to solve…

Q: Find the maximum and minimum values of the function f(x,y)=2x^2+3y^2−4x−5 on the domain x^2+y^2≤9.

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Q: Find the particular solution for ysqrt(1-x^2) * y'-xsqrt(1-y^2)=0  when y(0)=1

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Q: Find the linearization of y=2^x at a=0

A: use derivative to find the Linearization of y

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: Show that y = x° + 3x +1 Satisfies y" + xy" – 2y' = 0.

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Q: 8. Find the extremum and saddle points of the function f(x, y) = x³ – 3ry + y³ if any

A: Given function is fx,y=x3-3xy+y3

Q: II- Find the local maximum and minimum values and saddle points of the 3y? 3xy - 2 function f(x, y)…

A:

Q: Find the linearization of the function at x = 1. * f (x) = 2x³ - 3x + 7 O y = 6 + 1(x - 3) O y = 6 +…

A: Given, fx=2x3-3x+7

Q: Verify that 0t ду дх дх ду 2. 3 y 3 f (x, у) %3D 2х*у — х"у — ху

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Q: 1 Find the length of the curve f(x) + from x = 2 to x = 4. %3D 6. 2x

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

A:

Q: Calculate fxyy for f(x,y) = x 3 + y2ex.

A: Given function is fx,y=x3+y2ex. To calculate: fxyy. Solution: fxyy means first partial derivative of…

Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: Q5- Show that are eventually fixed point for the function: '5' 4x 0 <x < く 2 - 4x <xく f(x) = 4х - 2…

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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: -2 The domain of f(x,y) = is %3D x² + y?

A: f(x,y)=-2x2+y2

Q: A 3 X Y- X Y = 4xソーメニ2findr 3D2 and X"at X =1

A: Using definition of differentiation

Q: 9. Find a quadratic function y = ao + a1x + a2x² satisfying y(1) = 1, y(-1) = 2, and y'(1) = 2.

A: put values and make equations then solve

Q: f(x) = { Sx + 2 1-x+3 x>-2 Dano

A:

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

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.