What is the length of the shortest edge of the box if it has a volume of 30 cubic units?

Question

The volume of a box can be found with the function V, where x is the length of the shortest edge of the box:

 

V(x) = x³ + 5x² – 14x

 

What is the length of the shortest edge of the box if it has a volume of 30 cubic units?

Answer 1

V = x(x^2 + 5x -14) = x(x+7)(x-2) = 30

shortest side x = 3

x+7 = 10

x-2 = 1

It's 3x10x1 = 30