Determine the vertex- f( x)= x^2 +4x +3 O (2-1) (-2, -1) O (3,-1) O (1,-2)

Q: Find two positive integers whose sum is 16 and the sum of whose squares is minimum

A: Given sum of two numbers are 16. Let first number be x and second number=16-x. Now, sum of squares…

Q: Estimate and classify the critical points for the graph of the function. 4. -4 1-2 4 -2

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Q: what is the maximum/minimum of: f(x)=5x3e-x on [-1,6]

A: Differentiate the given function with respect to x and find the critical points,

Q: Find the maximum and minimum value of x3+y3-3axy

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Q: Find two positive integers such that their sum is 10 and maximize and minimize the sum of their…

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Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

Q: Find two real numbers whose difference is 40 and whose product is a minimum.

A: Let the two real numbers be x & y. Since the difference is 40, therefore x-y=40⇒y=x-40   →1 Now…

Q: Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: First make equation and then differentiate

Q: Where is optimization often applied and what is its importance?

A: Solution:Optimization:Optimization methods are used in many areas of study to find solutions that…

Q: find the maximum and minimum values of the func- tion on the given interval y=2x2−4x+2,  [0,3

A: Given y=2x2-4x+2

Q: 12. Of all numbers whose sum is 70, find the two that have the maximum product.

A: let x and y be two numbers whose sum is 70   we have to maximize  M=xy where x+y=70

Q: A rectangle is bounded by the x- and y-axes and the graph of y = (5 - x) / 2 . What length and width…

A: Given, A rectangle is bounded by the x-axis and y-axis and the graph of y=5-x2

Q: Solve using optimization 2. Find a pair of non-negative number that have a product of 162 and…

A: Solved below

Q: Estimate and classify the critical points for the graph of the function. 4. -4 2

A: A critical point of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: Find two positive numbers whose sum is 14 and the sum of whose squares is minimum

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

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Q: Provide two positive numbers with a product of 169 and a sum which is a minimum.

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Q: How can you apply the chain rule in calculus 3 with multivariable calculus

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Q: Find the minimum of f(x) = 3 + 6*x + 5*x2 +3*x3 + 4*x4 in the range of [-2, 1]

A: the given function is f(x)=3+6x+5x2+3x3+4x4 find the derivative  f'(x)=6+10x+9x2+16x3 find the…

Q: Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

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Q: Determine the equation of a quartic function that has zeros of −4 , 1 , and 2 (order 2) and passes…

A: The polynomial has the form f(x)=a(x-a1)b1(x-a2)b2....(x-an)bn

Q: 11. Of all numbers whose sum is 50, find the two that have the maximum product.

A: Let x and y be the two numbers.then,x+y = 50 y = 50-x            ..........(1)Let P be their product…

Q: Find the number in the interval [ - 5,5] so that the sum of six times the number and its square is…

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Q: : Let y = x3-3x + 2, find the absolute maximum and minimum on the closed interval [-3,3] and sketch…

A: Given  y = x3-3x+2 We have to find the absolute maximum and minimum on the closed interval [-3, 3].

Q: How do I find Sec(2) with minimal calculator use?

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Q: Find the three areas of the region bounded by y= 2x²+10 , y=4x+1 and the lines x=-2 and x=5.

A: We need to find the area between two curves. The area between two curves y=fx, y=gx for x∈a,b is…

Q: Find two positive numbers with product 256 and whose sum is a minimum

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Q: Forwarded Maximize z = 2x1 + 3x2 subject to 5x1 + 7x2 \leq35 4x1 + 9x2 \leq36 x1, x2 \geq 0 and…

A: Maximization of a linear programming problem is carried out to obtain a solution that follows all…

Q: The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of…

A: y = 0.013x2 - 1.19x + 28.24 We have to solve for the value of x when y = 10 Or, we have to…

Q: Suppose the point (-3, 10) lies on y = f(x) and the point (2, -3) lie point on the function y =…

A: Introduction: The function f(g(x)) or (f ∘g) represents the combination of functions f(x) and g(x),…

Q: piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

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Q: Maximize Z = 10x1 + 20x2; Subject to -x1 + 2x2 ≤ 15 x1 + x2 ≤ 12 5x1 + 3x2 ≤ 45 and x1 ≥0, x2 ≥ 0

A: Given -  Maximize Z = 10x1 + 20x2Subject to :-x1 + 2x2 ≤ 15x1 + x2 ≤ 125x1 + 3x2 ≤ 45x1, x2 ≥ 0 To…

Q: Find two numbers with difference 130 and whose product is a minimum.

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Q: What is the maximum value of y = -3.4sin(x- 60˚)?

A: we will use derivative.

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

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Q: Determine two positive numbers whose product is 4 such that the sum of their squares is minimum.

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Q: The mean of 5 positive integers is 16. What is th maximum value that one of this numbers may have?

A: Given problem is :

Q: Use Lagrange multipliers to find three positive numbers whose sum is 230 and whose product is…

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Q: Show that |x + y|≥||x|−|y||, solution without using piecewise function

A: Just I have used the triangle inequality of absolute function and easily prove that the given…

Q: A 40-room hotel is fully occupied if $3000 is charged per day per room. For every x hundred-dollar…

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Q: maximum

A: if you specifically asking to how to find maximum and minimum value. Please refer to the image below…

Q: 3x2 If (x) = x² + 1

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Q: graph of f(x) = 4(x – 2)² – 7 is a parabola that opens --Select- v with its vertex at (x, y) = ( and…

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Q: Find critical number of f(x) = 4x^2 + 8x -1

A: We have to find critical number of  f(x) = 4x2 + 8x - 1 To find critical number, differentiate f(x)…

Q: What is the general form of the chosen low or- der polynomial model?

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Q: Find the cxhreme Point and extreme direcbion region of the て-う + X2u5 2 (メメ): - 3X、 → X2c-2 -Xit…

A: We are given the following system of 2d Linear equations : -3x1 + x2 ≤ -2 -x1 + x2 ≤ 2 -x1 + 2x2 ≤ 8…

Q: Find two positive numbers with product 256 and whose sum is a minimum.

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