find the value of "x" that gives the greatest possible area of a rectangle? with a length of 3x inches and a height of (8-x)inches

Question

anonymous · Answer

you can also do 3x(8-x)=0 and find the y-coordinate of the vertex, then solve for x

anonymous · Answer

not =0, rather just find the vertex of 3x(8-x)

anonymous · Answer

Area is length times width; as a function of x,$$A(x)=3x(8-x)=-x^2+24x$$This function is quadratic, opening downward.  Its maximum is at the vertex, with x value 
x=-b/2a=-24/-2=12

anonymous · Answer

It seems the maximum area is just about 144 in^2.

anonymous · Answer

One thing I'm noting here is that the height of the rectangle works out to a negative number; I'm a little concerned about that......

anonymous · Answer

you took out the 3 for some reason from your calculation in the vertex

anonymous · Answer

I guess I've had enough math for today; can't even distribute properly any more...LOL

anonymous · Answer

lol

anonymous · Answer

the vertex has x-coordinate of 4, so the dimensions are 3*4 x (8-4) or 12 x 4

anonymous · Answer

Attempt number two:

$$A(x)=-3x^2+24x$$Maximum value at x=-b/2a=-24/-6=4

Maximum value about 48 in^2.