V(x)= 8x(6-x)(12-x)
The domain contains all permissible values of the function in the particular application. Since the box cannot have negative sides, so the domain should reflect that, nor can the side be negative.
Thus the domain of x is limited to values between 0 and 6, or (0,6), since a box of zero volume is meaningless.
Expand V(x) to a polynomial and differentiate to get the maximum volume. Do not omit to check that the value is indeed a maximum and not a minimum.
The polynomial, when expanded, is
8x^3-144x^2+576x
HELP!
The volume of an open-top box is given by V(x)= 8x(6-x)(12-x)
a) Give the domain for x.
b) Find the x that maximizes the volume for the box?
c) What is the maximum volume in cubic inches?
1 answer