Question

Find de 60 X 2 X X=12 X 3 X x? 120x - 36x4 d. Find the value of x for which V is a maximum.

Answer 1

y=20-4x

Then the volume is

`V=\mleft(3x\mright)\mleft(x\mright)\mleft(20-4x\mright)`

`V=60x^2-12x^3`

The derivate of the V

`(dV)/(dx)=120x-36x^2`

In order to find the value of x where V is a maximum, we need to find the value when the derivate is 0

`x(120-36x)=0`

we have two options

x=0 and

120-36x=0

120=36x

36x=120

x=120/36

x=10/3

Then we evaluate these values into the Volume equation

First x=0

`V(0)=60(0)-12(0)=0`

The x=10/3

`V((10)/(3))=60((10)/(3))^2-12((10)/(3))^3=(2000)/(9)=222.22`

the maximum Volumen is when x=10/3=3.33