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

$\frac{dV}{dx}=120x-36x^2$

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

$V(\frac{10}{3})=60(\frac{10}{3})^2-12(\frac{10}{3})^3=\frac{2000}{9}=222.22$

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