A rectangle is constructed under the graph of f(x)=4x2with one corner at (7,0) and one corner on the graph of f(x)= 4x2where 0≤x≤7 Find the exact value of xx that will maximize the area of the rectangle. x=

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Q: A rectangle is constructed under the graph of f(r) = 4x with one corner at (7, 0) and one corner on…

A: Consider the rectangle. The top left corner of the rectangle lies on the curve y=4x2. Thus, the…

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Q: 2. Of all numbers whose sum is 30, find the two that have the maximum product. That is, maximize Q =…

A: To Determine: of all numbers whose sum is 50 ,find the two that have the maximum product .That is…

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Q: Of all numbers whose sum is 46, find the two that have the maximum product. That is, maximize Q = xy…

A: Given ,           x+y=46           Maximize , Q=xy

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Q: Find the critical points of the function f (x) = 2x³ – 9x² +12x+47. Show all your work.

A: Firstly we find the derivative of the function and then put it equal to zero and find the x values…

Q: Find the point on the graph of y = 1x that is closest to the point (2, 0). [Hint: 2(x - 2)2 + y2 has…

A: Given: y=x Let the point closest to (2,0) be P(x,y). Distance between point P(x,y) and (2,0) is:…

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Q: Of all numbers whose sum is 52, find the two that have the maximum product. That is, maximize Q = xy…

A: Given, Q=xy                        ...(1) Where x+y=52⇒y=52-x                            ...(2)

Q: Suppose a corporation manufactures candles at two locations. The cost of producing *1units at…

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A: we have been given the function of a volume V(x)=(10-2x)(16-2x)x  where x=side of square pieces that…

Q: find the critical points and determine whether they are minima, maxima, or neither f (x) = x3 − 4x2…

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Q: Find two positive numbers x and y that maximize Q = x2y if x + y = 2.

A: Given function - Q = x2y               ...........(1)And,x+y = 2y = 2-x…

Q: 1. Of all numbers whose sum is 70, find the two that have the maximum product. That is, maximize Q =…

A: Let such two numbers whose sum is 70 and have the maximum product are x and y. So, we have x+y=70…

Q: Find the critical points and determine whether they are minima, maxima, or neither: f (x) = x2/3(1 −…

A: Given: fx=x231-x

Q: Of all numbers whose sum is 46, find the two that have the maximum product. That is, maximize Q = xy…

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Q: Find the relative maxima or minima. Maximum of ƒ(x, y) = x2 - 5y2, subject to x - y = 12

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Q: The cost of producing x units of a certain commodity is C(x) = 1x² + 5x+8 dollars. If the price is…

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Q: Where does A(x) have a maximum? Explain why that answer is what you should have expected.

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Q: Find the absolute minimum and absolute maximum for y = x3 – -+ 4x +1 on [-2,2].

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A: Here I am attaching image so that you understand each and every step.

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Q: Find the maximum area of a rectangle inscribed under f(x)=16-x2 and the x axis

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Q: Minimize F = 24x2 + 24y2 with xy2 = 16.

A: Minimize F = 24x2 + 24y2 with xy2 = 16.

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Q: Find the absolute extrema of the function on the closed interval. 3x2 g(x) [-3, 2] X - 6 minimum (x,…

A: Given, gx = 3x2x-6           -3, 2 We have to find the absolute extrema of the function in the given…

Q: Use langrage multiplier to maximize f(x,y)=25- x2 -y2 subject to 2x+y=10

A: We have f(x,y) = 25 -x2 -y2 subject to 2x + y =10

Q: What is the absolute minimum value of q(x) = 2x -1 over -2, 5?

A: We have to find the absolute minimum value of q(x) = 2x2 - 1 over [-2, 5].

Q: Find the point P on the line y = 5x that is closest to the point (52,0). What is the least distance…

A: Given that point P lies on the line y=5x. We need to find : i) the point P on the line y=5x that is…

Q: Of all numbers whose sum is 54​, find the two that have the maximum product. That​ is, maximize…

A: we have to find the value of x and y when Q has maximum value. the solution is following.

Q: A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular…

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Q: A piece of cardboard measuring 14 inches by 9 inches is formed into an open-top box by cutting…

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Q: Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4]

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Q: Find the minimum and maximum of x3+3x². on the interval [0, 3].

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Q: Suppose x and y are positive integers such that the sum of x^2 and y is 10x. Find the values of x…

A: Given x^2+y=10x.From there find y.

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

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