Postal Restrictions If a box with square cross section is to be sent by the postal service, there are restrictions on its size such that its Volume is given by V= x²(108-4x), where x is the length of each side of the cross section (in inches).
(a) Is V a function of x?
(b) If V= V(x), find V(10) and V(20).
(c) What restrictions must be placed on x (the domain) so that the problem makes physical sense?
V = x^2(108 - 4x)....(1)
Yes V is a function of x, because the value of V depends on the value of x. x is the independent variable ad V is the dependent variable.
So we can write, V = V(x) = x^2(108 - 4x)
V(10) = 10^2(108 - ...
This looks at the restrictions of a function for a given situation (mailing a package).