Question

A warehouse stores rectangular shipping containers with side lengths of 4x ft, 5x ft, and 6x ft. The function f(x) = 3x2 models the cost, in dollars, for storing each container. What are reasonable domain and range values for f if the length of a container’s longest side can be no more than 90 ft?

domain:
< x ≤


range:
< f(x) ≤

Answer 1

Longest side = 6x ≤ 90 → x ≤ 15. x must be positive, so domain: 0 < x ≤ 15.

f(x) = 3x^2 so max f at x = 15: f(15) = 3(15^2) = 675. With x>0, range: 0 < f(x) ≤ 675.