MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A printed page is to contain 192 cm2 of text. The page has uniform margins of 2 cm at the top and bottom and 1 cm on each side. Let the width and height of the entire page be x cm and y cm respectively.
(a) Express the total area A of the page in terms of x only.
(b) Determine the dimensions x and y that minimise the amount of paper used.
(c) Establish, by applying the second derivative test, that your answer in part (b) corresponds to the minimum possible paper area.