A model of carry-on luggage has a length that is 15 inches greater than its depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 35 inches. These conditions, with the assumption that this sum is 35 inches, can be modeled by the function 𝑉(𝑥) that gives the luggage’s volume, in cubic inches, in terms of its depth, 𝑥, in inches. Use the graph of 𝑉(𝑥) to the right to complete parts (a) and (b) below.

Volume depth

𝑉(𝑥),=,𝑥

𝑉(𝑥),=,𝑥(𝑥+15)(20-2𝑥)2

length * width: 35- (depth + length