1. Find the maximum and minimum points of the given equation: a. y = x3 – 3x b. y = (x – 6)2(9 – x)

Q: Find the abscissa of the point on the graph of y=V 2x – 1 that is parallel to the line 2x - y+1=0

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Q: (b) Determine the position and character of the double points on the curve x³ + x² +y² – x – 4y +3 =…

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Q: 1 2 #5) A) Find the length of a curve y Inx for 3 < x < 7. 4

A: L= integration of sqrt of 1+ (dy/dx)2 dx from a to b

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: Find the exact length of the curve. y = 3 + 2x^(3/2), 0 less than x less than 1

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Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

Q: Find the relative maximum and minimum values. ​f(x,y)= x^3+y^3-33xy

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Q: c. What is the maximum or minimum point for the curve y = -3x2 - 12x + 5?

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Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

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Q: Find the x- coordinate of the inflection point(s) of the | .2* curve y = -7xr'+ 4x +10.

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Q: 5. y2 2x y26-x fx, y) = 4x+ 3y Minimum: Maximum: | | | | |

A: We need to find maximum and minimum values of f(x,y).

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: Find the points on the curve x^2y = 2 nearest the origin.

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: The x coordinate of the point of intersection between the two curves Y e14a and y = 1 is = x =

A: Given: y=e14xy=1

Q: Q1 Find thr relative maximum and minimum of: fx, y) = x² + y² + z?given that 9x? + 4 y² + 2z? = 36…

A: Consider the provided question,  minimize and maximize, fx,y,z=x2+y2+z2                        ....1…

Q: z = 3x' +1.5 y² – 18.xy +17 Find the extreme value and check whether it is maximum or minimum.

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Find the point on the parabola x = t, y = t2, -infinity&lt;=t &lt;=infinity, closest to the point…

A: Consider the required point as (x,y)Consider the formula of distance between the two points.

Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: f(x, y) = 2x2 + 3y2 - 4x - 1, x2 + y2 s 16 maximum minimum

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Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

Q: 1 14y" – 15y/ + y = 0, y(0) = 14, y'(0) 14 Then determine the maximum value M of the solution and…

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Q: Find the relative maximum and minimum values. f(x,y) = x +y - 2x + 10y – 14

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Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

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Q: Find the relative maximum and minimum values. f(x,y) = 3x² – 4y?

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Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Q3) Find the local maximum and minimum points of the following curve: y = 3x + 2x? - 4x + 2

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Q: Find the extreme values of g(x,y,z) = 2x² + xy + 4y² + xz + z² + 2. %3D and determine whether the…

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Q: Find the relative maximum and minimum values. Зx2 f(x,y) = + 10y2 + 3

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Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

A: The points where the tangents are horizontal are the points at which slope is zero.That means,…

Q: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

Q: B. Find the length of the curve y= x2 from x = 0 to x = 7.

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Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: For y> 0, find the minimum value of + 10 +5y2 5 y2

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Q: Given the parabola: x2+12y=0 and the tangent line x+y-3=0, find the point of tangency

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Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y &gt; 0

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Q: Given f(x, y) = x² – 4y, the parabola x - 4y = 8 = 0 is the level curve o -8 None of the given…

A: The solution is given below

Q: A. Find an equation of the level surface of f(r, y, 2) = 4.x2 + 22 that passes through the point…

A: Given:     f(x,y,z) = 4x2 + z2      Point: ( 1 , 2 , 3 )

Q: 11. The maximum point of the curve * y =r' - 3r° + 4 is at

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Q: Find the minimum and maximum values of the function f(x, y, z) = 5x + 6y + 4z subject to the…

A: Here we have f(x,y,z)=5x+6y+4z subject to the constraint x2+6y2+6z2=1 Let g(x,y,z)=x2+6y2+6z2-1

Q: 1 + 12 8x*' - Find the length of the curve y= 1<x<2. 4

A: y=x612+18x4 Differentiate the  above equation dydx=ddxx612+18x4dydx=x52-121x5

Q: Q5) Find the absolute maximum and minimum values of D(x,y) = x² - xy + y² + 1 On the closed…

A: Given: D(x,y)=x2-xy+y2+1

Q: Find the absolute maximum and minimum values f(x, y) = x2 + 4y2 - 2x - 8y + 1, D

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: (c) Given that y = x4 – 8x²

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Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12