(1) Find a point P in the first quadrant on the curve f(x) = 3 such that the rectangle with sides on the coordinate axes and a vertex at P has the smallest possible perimeter. %3D

Q: The region between the graphs of f(x)=x^2+3 and g(x)=−x+5 has ____________area square units.

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Q: Find the local minimum and maximum of y= x2/ 3 + x2

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Q: 5. Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

A: Answer

Q: 3. The region between the graphs of y = x3 + 4x - 1 and y = 2x3 + 3x? - 1

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Q: Is the point a = [0, 1]T a local minimizer? %3D

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Q: Use Lagrange multipliers to find the point (a,b) on the graph of y = e4x, where the value ab is as…

A: Let the objective function fx,y=xyand the constraint function…

Q: The area of the largest rectangle that can be drawn with one side along the x-axis and two vertices…

A: The diagram below shows the rectangle as mentioned in the problem, The rectangle is symmetric about…

Q: A cable runs along the wall from C to P at a cost of $14 per meter, and straight from P to M at a…

A: Given that the length from C to P is ‘x’ find out the value of x , so that the cost of installing…

Q: if y=x to the 3rd power - 3x. find the maximum value of y? -1

A: Given

Q: 10. Use Lagrange multiplier to find the point(s) on the circle x² +(y-1)´ = 9 closest to the point…

A: Given circle isx2+y-12=9  and point is (4,4) solve it by using Lagrange multiplier find the closest…

Q: g(x) = Vx is reflected over the y-axis and vertically compressed by a factor of ¼ %3|

A: Given function is gx=x We have to find the transformed function which is reflected over the y-axis…

Q: Find the point on the graph of y = 2x that is closest to the point (3, 1). Use distancefrom and…

A: Let the point on the graph of y = 2x be (a,2a). Now, Using the Distance formula between two points…

Q: Question 7 Consider the Quadratic function f(x) = 9x² 4. Its vertex is ( Its largest z-intercept is…

A:

Q: A wire that is 16 centimeters long is shown below. The wire is cut into two pieces, and each piece…

A: Topic:- calculus

Q: 12) A manufacturer has determined that the total cost C of operating a factory is C= 3x² + 70x +…

A: We have given: The total cost C(x) = 3x2 + 70x + 2700, where x is the number of units produced.

Q: Find the area of a triangle bounded by the y axis, the line f(x)=4−(6/7x) and the line…

A: Formula Used: Area of triangle is :                                   Where,  b is base of triangle…

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: *Sotve the fotowing tineat optimization Problem using the Latge M me thod- Max Z=Xx+8X2 Subject to…

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Q: If g'(x) =-3x(x+2), then the graph of g(x) has a relative maximum at what value(s) of x?

A:

Q: A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6 mi from…

A:

Q: Consider the problem f (x) subject to g;(x) = 0, minimize %3D

A: Given, the problem                 minimise f(x)            subject to   gi(x)=0, i=1, . . ., l…

Q: In p(x,y) = 3ry – x* – y°, x is the average daylight and y is the average daily rainfall. %3D Solve…

A: To find the points that maximize the the productivity of the function px, y=3xy-x3-y3

Q: 2. Find the least quadratic fit of the form y = ax² + bx +c for the data. Set up by hand. Solve…

A:

Q: 1. The graph of f(x) = 2x3 + x² – 20x + 1 has a relative minimum at A. x = -2 C. x = 2 D. x = 1 ק…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: The graph of f(x) = 5(x - 3)2 - 2 is a parabola that opens upward with its vertex at (x, y) = | and…

A: We have to find the vertex of the parabola and its minimum value.

Q: 5. Create a graph of the function: t -1 %3D x+2 Ay

A: Given:         Equation is y=-1x+2below graph is plotted using online tool

Q: The region in the first quadrant bounded by the x-axis and f (x) = 3x – x² is

A: The graph of region bounded by curves y=3x-x^2 and x-axis is

Q: 1. The Maximum point of y = (x²+2x+10) (x-3)

A: Find out the maximum point.

Q: A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 15 mi from…

A: Given- A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 15…

Q: Locate the critical points, and determine the maxima and minima. y = x2(x - 2)2.

A:

Q: 20. A closed rectangular box with a volume V cm³ . The cost of materials used in the box is a…

A: Minimization using AM GM inequality

Q: The graph of f(x) = mx - 3x - nx +5 has a relative maximum at (-1,12) and a point of (1 3) 2' 2…

A:

Q: 2. Find an equation of the form f(x) =b.a +c that has the horizontal asymptotes at y = 350,…

A: y=b is said to be a horizontal asymptote of a curve y=f(x) if as x tends to infinity (or -…

Q: A boat on the ocean is 5 mi from the nearest point on a straight shoreline; that point is 12 mi from…

A: Given a boat in the ocean is 5 mi from the nearest point on a straight shoreline that point is 12 mi…

Q: b) Find all points of local maxima and local minima of the function f(x) = x' – 3x + 3.

A: We use application of derivatives to solve this problem.

Q: Find the values of constants a, b, and c so that the graph of y = (x2 + a)/(bx + c) has a local…

A: given

Q: A rectangle has one side on the x-axis and the upper two vertices on the graph of y = e 42. Where…

A: Here we have a rectangle that has one side on the x-axis and the upper two vertices on the graph of…

Q: A boat on the ocean is 2 mi. from the nearest point on a straight shoreline; that point is 13 miles…

A: According to the question, x is the distance between the nearest point on a shoreline and the point…

Q: Use Lagrange multipliers to find the point (a,b) on the graph of y = e^(5x) where the value ab is as…

A:

Q: Please

A: The given function is

Q: Determine equation in factored form for the function, f(x), shown on the graph. y Intercept (0,6)…

A: By looking at the graph it can be said that the function is of order 3. Here, the x-intercept is…

Q: Find all the local maxima, local minima, and saddle points of the function. 4x² + 4y² - 32x f(x.y) =…

A:

Q: 1. The Maximum point of y= 9-x² x²-4

A: This is a problem related to maxima and minima. Based on the general formula and concept we will…

Q: 12) A manufacturer has determined that the total cost C of operating a factory is C= 3x? + 50x +…

A: We first find the average cost function

Q: A closed rectangular box with a volume V cm. The cost of materials used in the box is a sen/cm? for…

A:

Q: Q4. Solve graphically. minimize 4x, + 2х, Subject to: х, + 2х, 2 2; Зх, + х, 2 3; 4х, + 3x, 2 6; X;;…

A: Given: 4x1+2x2=Z Subject to constraints : x1+2x2≥2 3x1+x2≥3 4x1+3x2≥6 x1;x2≥0

Q: Find all local maxima, local minima, and saddle points for z = x² + xy + y² – 6x + 6.

A:

Q: 6. (a) Maximise f (r, y) = 2r + y subject to 2a2 + y = 1 (b) Minimize f(r, y) = 2r + y subject to…

A:

Q: find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. kx2…

A: The given family of curves is kx2+y2=1. Differentiate both sides of the above equation with respect…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.