Question

Can someone please help me?!

Answer 1

V=x(8-2x)(10-2x) or expanded

V=x(4x^2-36x+80)

V=4x^3-36x^2+80x

...

If you were to graph the above equation for V(x) you will see a maximum point where the "y" value is maximized, but be careful as V will increase without bound at values of x that are not part of the domain, ie, in this case x<8/2, x<4 to have any meaning...The proper domain of this function is:

x=(0,4), Mathematically finding this point quickly is by differentiating it with respect to x...

dV/dx=12x^2-72x+80, The maximum volume will occur when dV/dx=0 and the x value is within the correct domain...

12x^2-72x+80=0  (using the quadratic formula for ease)

x=(72±√1344)/24, and since x<4

x≈1.472in  (to the nearest one thousandth of an inch)