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...
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: