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...crying

 Oct 15, 2020

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:


 Oct 15, 2020
edited by ElectricPavlov  Oct 15, 2020
edited by ElectricPavlov  Oct 15, 2020

uugghh!!..wink..so my main error really was coming to the correct expression for the area, from there I could manage...blush..Thanx once again ElectricPavlov!

juriemagic  Oct 15, 2020

Yeppers !   Math on......

ElectricPavlov  Oct 15, 2020

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