An open-top rectangular box with a square base is to be constructed from of material
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
An open-top rectangular box with a square base is to be constructed from 1200 cm2 of material. All material is used for the five faces of the box (four sides and the base).
(a) Let x be the length of a side of the square base in centimeters, and let h be the height of the box in centimeters. Express the volume V of the box as a function of the single variable x by eliminating h.
(b) Determine all critical values of V on the admissible domain for x.
(c) Use the second derivative to verify that the critical value found corresponds to a maximum volume for the box.
(d) State the dimensions of the box that maximize its volume and compute this maximal volume to the nearest cubic centimeter.