Answer:
x is 10
Step-by-step explanation:
- Let x is the side of the base
- Let h is the height
Given that:
- The area A = 4200 cm2
<=> 2 + 4xh = 4200 cm2
<=> 4xh = 4200 - 2
<=> h = (4200 - 2 )/4x
- The volume of the box:
V = h
<=> V = (4200 - 2
)/4x
<=> V = (4200x - 2 )/4
- To find the maximum volume, we differentiate volume with respect to x:
dV/dx = (4200 - 6 )/4
Set dV/dx = 0, we have:
4200 - 6 =0
<=> = 700
<=> x = 10
- We differentiate again
d²V/dx² = -12x/4
It is negative so the volume is maximum.
So x is 10