Find maximum point and minimum point for у 32x3 -3x2-12х +8

Q: The sum of two numbers is 5. Find the minimum value of the sum of their cubes.

A: Let the first number be x. Let the other number be y.   Thus, x+y=5y=5-x   The sum of the cubes of…

Q: The sum of the length and girth (perimeter of a cross section) of packages carried parcel post…

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The extrema of a…

Q: 2. What is the minimum product of two numbers that differ by 15? What are the two numbers?

A: Let one number be x and another number be x+15 So their product=x(x+15)=x2 + 15x =f(x) (say)

Q: minimum point

A: We say that f(x) has an absolute (or global) minimum at x=c if f(x)≥f(c) for every x in the domain…

Q: The sum of two numbers is 6. Find the minimum value of the sum of their squares.

A: The sum of two numbers is 6. Find the minimum value of the sum of their squares.

Q: Find two numbers whose difference is 100 and whose product is a minimum.

A: Find two numbers whose difference is 100 and whose product is a minimum

Q: Find the dimensions of the rectangle of maximum area which can be laid out within a right triangle…

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Q: A rectangular hole is to be cut in a wall for a vent. If the perimeter of the hole is 104 in. and…

A: Let, Length = L inches. Width = W inches. Given that the perimeter = 104 inches. That means:…

Q: A farmer has 600m of fence to enclose a rectangular divided pasture adjacent to an existing wall. He…

A: In question given that  farmer has 600m of fence to enclose a rectangular divided pasture adjacent…

Q: Find two numbers with difference 90 and whose product is a minimum

A: Solution: The objective is to find the two numbers with the difference 90 and whose product is a…

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A: Let us assume the side of bird sanctuary along the river side is x km and other side is y km. Since,…

Q: Rudgene Claire, the President of Women's Association of their barangay, proposed a project: to put…

A: Give that the perimeter of the lot is 40 meter. Let x be the length of the rectangular lot  and y be…

Q: Identify the following properties of the quadratic equations: 1) AOS 2) Vertex 3) minimum/maximum 4)…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: 4=-Y36x-4)'+2 (4,2). Equation #15 maximum or minimum

A: Given function is,

Q: Find two numbers whose sum is 10, and the sum of whose squares is a minimum. Please put the…

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Q: Find the dimensions of the rectangular box of maximum volume if the sum of the length, width, and…

A: To find dimension of the rectangular box of maximum volume  Given sum of length, width and height…

Q: 3. Determine the number of points of intersection of the linear-quadratic system. y 2x-8 y 3x2 + 12x…

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Q: x +y + 2z=1 2x-y-z = 0 x +2y-z = 4

A: Follow the steps below.

Q: Rudgene Claire, the President of Women's Association of their barangay, proposed a project: to put…

A: Let x and y be the length and width in meters be the length and width of the rectangular garden.…

Q: What is the minimum product of two numbers that differ by 15? What are the two numbers?

A:

Q: A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

A: Here we can note the following  (a) Area of an equilateral triangle with side a = 34a2 Area of a…

Q: A package in the shape of a rectangular box can be sent by post as a postal order if the sum of its…

A: Solution by using Lagrange multipliers as follows :

Q: If the sum of two different positive numbers is twice your age, what is the maximum product of them?

A:

Q: What is the maximum number of real solutions a system of equations composed of a linear function and…

A: Quadratic function has a degree 2 and linear function has a degree 1.

Q: 2. Write the constraint and the optimization equations.

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: A rectangle with length L and width W is cut into four smaller rectangles by two lines parallel to…

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Q: Find two numbers whose sum is 10, and the sum of whose square is minimum.

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Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A:

Q: The sum of two numbers is k. Find the minimum value of the sum of their cubes.

A: Answer and explanation is given below...

Q: Find three numbers whose sum is 9 and whose sum of squares is a minimum. The three numbers are.

A:

Q: The sum of the perimeters of an equilateral triangle and a square is 23. Find the dimensions of the…

A: let the side of equilateral triangle is x and side of square is a. therefore according to…

Q: a store can stock a maximumof 210 of tires, hubs and car seats. they know from past experience that…

A: According to the given information, Let the number of hubs be ‘x’ Then the number of tires be ‘2x’…

Q: Of all numbers whose difference is 6, find the two that have the minimum product.

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Q: Find two numbers whose difference is 20 and whose product is a minimum.

A: Given informationDifference of two no. is 20

Q: A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

A:

Q: The sum of the perimeters of an equilateral triangle and a square is 18. Find the dimensions of the…

A: Given that the sum of perimeter of equalatral triangle and square=18To find :dimention of…

Q: Find two numbers whose difference is 8 and whose product is a minimum.

A: Let x and y be the required numbers.  Given that the difference of the numbers is 8.

Q: Find two numbers whose difference is 100 and whose product is a minimum

A: To find the two numbers whose difference is 100 and whose product is a minimum Given information:…

Q: A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle,…

A:

Q: . The sum of two numbers is b, what is the minimum value for the sum of their cubes?

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Q: The perimeter of a rectangle is to be no greater than 100 centimeters and the width must be 15…

A: Perimeter of rectangle = 2 ( length + width)  Given width = 15 cm  and  perimeter of a rectangle…

Q: Find three numbers whose sum is 9 and whose sum of squares is a minimum.

A: Construct a system for optimization using the information that, the three numbers whose sum is 9 and…

Q: A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle,…

A:

Q: Show detailed solution. x² +x-12 Minimum point of y = x² -4

A: Given: y=x2+x-12x2-4

Q: Find two numbers whose sum is 10. and the sum of whose squares is minimum 3, 7 4, 6 5, 5 2, 8

A: Let first number is x and second number is 10-x for finding minimum then take it's derivative equal…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other sides by a…

A:

Q: The sum of the perimeters of an equilateral triangle and a square is 23. Find the dimensions of the…

A: Let x be the side of equilateral triangle and y be side of square . Then respective perimeters are…