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# Hi friends,

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Hi friends,

The below picture is taht of a line, y=2x and x=4 We have to find the largest area.

I named pq = x and ps =y

So, the Area=xy

but y=2x, so

the Area is \(2x^2\)

To get the max area, we have to find the 1st dirivative, which is \(4x\)

then equate this to 0, to find x

So x end up being 0....where am I going wrong please please... Oct 15, 2020

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Area =2x  * ( 4-x)    over the domain  x = 0 to x = 4

Area =  8x - 2x^2

you want to find the maximum value of this function (which is a dome shaped parabola) from x = 0 to x = 4

you can graph it ...or calculate the max value of x    that produces the max area (the vertex)

- b /2a = -8/(2* -2) = 2         so x value of vertex = 2      plug this in to the area equation to find y = area = 8 units^2

Or if you want to do the derivative and set = 0

-4x + 8 = 0

x = 2     this is where the slope of the parabola is 0 ...this   is the x value which gives the greatest area....the vertex of the parabola....

you will have to plug this value of x into the area equation to calculate what the max area is when x = 2

8x-2x^2   = y  = area = 8 units2

Here is a graph of the area function:

https://www.desmos.com/calculator/mzd3s0ecs2

Oct 15, 2020
edited by ElectricPavlov  Oct 15, 2020
edited by ElectricPavlov  Oct 15, 2020
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uugghh!!.. ..so my main error really was coming to the correct expression for the area, from there I could manage... ..Thanx once again ElectricPavlov!

juriemagic  Oct 15, 2020
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Yeppers !   Math on......

ElectricPavlov  Oct 15, 2020