Find a function r(t) that describes the line segment from P(8,7,8) to Q(0,7,5) (inclusively). r(t) = (- 8t + 8, D, for

Q: A particle is moving along a straight line, whose directed distance from its origin is given by the…

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Q: The cost C of manufacturing transformers in a factory varies with the output N per day according to…

A: maxima minima question, if it is helpful, like and thumbs up.

Q: Find y as a function of t if 9y" +12y + 29y = 0,

A: 9y''+12y'+29y=0which condition y(2)=8, y'(2)=9To Find: y(t)

Q: Find the area of a triangle bounded by the y axis, the line f(z) = 9 -1, and the line perpendicular…

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Q: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

A: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

Q: Find d2y/dx2 as a function of t if x = t - t2 and y = t - t3

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Q: For an F-curve with df = (20, 21), find a. F0.01. b. F0.05. c. F0.10.

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Q: Differentiate the function with respect to y. A Z = + Bey уб Z' + Bey = 8A 9 y 20 -

A: In this question we have to differentiate the function with respect to y.

Q: Find the linear approximation of the function f(x) = Vx+3 at a = 1 and use it to approximate the…

A: Given the function fx=x+3. Find the linear approximation of f(x) at a=1 and use it to approximate…

Q: Find a function r(t) that describes the line passing through P(9,2,9) and Q(3,6,5). (1) = (- 6t + 9…

A: 0<t<1

Q: -16t +30t + 4 models the height of a ball t seconds of change of the function over the interval 0,2…

A:

Q: Find the extremum points of the function f(x,y) = y² +x*y +x² - 2y and determine the nature of the…

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Q: find the orthogonal trajection of the family of curves x2+y2=a2

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Q: Find y as a function of t if 5y′′+31y=0 y(0)=4,y′(0)=7y(t)=

A: The given differential equation is  5y''+31y=0   ......(1) and the initial condition is y(0)=4 and…

Q: Q2) Find Fxx, Fyy and Fyx For the function F(x,y) = (x+y) (y + 1)* .

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Q: 5 уx(1-3 ху) )= 1+xy el punto (1,8) y úsela para estimar f(1.2,8.2).

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Q: Find y as a function of t if 8y′′+32y=0 y(0)=9, y′(0)=6.

A:

Q: Find the values of x, y, and z that maximize the function 6xyz f(z, Y, z) = z + 2y + 2z' where a, y,…

A: Given: f(x,y,z)=6xyzx+2y+2z and condition is xyz=16

Q: Find y as a function of t if 324y′′+684y′+361y=0, y(0)=9,y′(0)=9.

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Q: 2017 F Q2 Find the set of values of k for which the line y = 3x + k and the curve y= 2x- 3x + 4 do…

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Q: An object moves along a horizontal line according to s (t) = 5t° – 2t², when is V increasing and…

A: In the given question, concept of derivative is applied. Derivative The derivative expresses the…

Q: Suppose f is a linear function such that f(3) = 3 and f(6) = 18. What is the slope m of f?

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Q: How many saddle points does the function f(x, y) 116 – 18r 66y + 9x + 11y? have? Answer: (Input 0 if…

A: Given problem:- How many saddle points does the function f(x, y) =116 - 18x - 66y + 9x2 + 11y2 have?…

Q: Find y as a function of t if y(0) = 7, (0) = 6. y(t) = = 49y" + 140y + 136y = 0,

A: The given DE is: 49y''+140y'+136y=0 So, the auxiliary equation of it is:…

Q: For an F-curve with df = (6, 10), find a. F0.05. b. F0.01. c. F0.025.

A: Using Excel, The vale for the F-curve with df = (6,10) is shown below

Q: Find a function y(x) such that 4yy' = x and y(4) = 6

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Q: For the function f(x,y,z) = 3 + xy5 - 5z4, find fx , fy , and fz.

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Q: Find y as a function of t if 4y" + 40y' + 100y = 0, and |У(3) — 6, у'(3) —D 7.

A: Given differential equation is Characteristic equation of the differential equation is Therefore,…

Q: Find the linearization for f(r) 10, and use it to approximate 12 near a=

A: We want to find the approximate value of 112 by linear approximation of the function ,fx=1x by…

Q: The position function of a particle is given by 7(t) = (t², 5t, t2 – 16t). When is th sneed a…

A: Given:

Q: Find dz implicitly of the relation r + y³ = 3ry.

A:

Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

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Q: Find the orthogonal trajection of the family of curves x2+y2=a2

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Q: Q5: Find the max and min points for the function: F(x,y) = x2+xy2-4x+1

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Q: Show that f is linear of slope m if and only iff(x + h) - f(x) = mh (for all x and h)

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Q: Find an equation for the linear function g(z) which is perpendicular to the line 7z – 6y = 12 and…

A: Given the equation of a line 7x−6y=12

Q: f(x) = + 3, X with 0 < x< 3

A: The length(arc-length) of the function is given by: L=∫ab1+(f'(x))2dx

Q: Find y as a function of t if 64y" + 144y' + 106y = 0, y(0) = 8, y' (0) = 3. y =

A: Given DE is  64y''+144y'+106y=0.....(1) Initial conditions are  y(0)=8,y'(0)=3......(2)

Q: Find y as a function of t if 8y" + 29y = 0, y(0) = 5, 3'(0) = 8. y(t) =

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Q: Find y as a function of t if 7y" + 32y = 0, y(0) = 2, y'(0) = 4.

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Q: Find a function y(x) such that 4yy' = x and y(4) = 7.

A: Answer

Q: of the function. + 3y + 11

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Q: - Find the Absolute Max and Absolute Min of the function f(x, y) = 5x2 – 3y2 on the disk r+ys 100.

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Q: Find a function r(t) that describes the line passing through P(5,4,5) and Q(7,9,3). r(t) = (2t +…

A: The parametric function r(t) is represented with r(t)=P1+(P2-P1)t

Q: Find y as a function of t if 9y" + 12y' = 0, y(0) = 3, y'(0) = 3. y = 3e^(-4/3t)+3

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Q: (b) Find the Linearization of the function: f(x)= Vx at a= 27 and use it to approximate the number…

A: Let the function is f(x)=x3 Let a = 27   Formula: Linearization of the function f(x) at x = a…

Q: Consider the function f(x, y) = 4x² – 8y² subject to the condition x + y = 25.

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Q: Find y as a function of t if y(0) = 4, y(0) = 9. y(t) = 576y" +624y + 169y = 0,

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.