MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
For a rectangle, the width is always half of its length, that is y(t)=21x(t).
When the length is 12cm, the perimeter is increasing at 1.6cm s−1.
(a) Find the rates of change of the length and width at this instant.
(b) Hence determine the rate at which the area of the rectangle is changing at the same instant.
(c) Suppose instead that the perimeter were decreasing at 1.6cm s−1 while the length is still 12cm. Without repeating the whole calculation, state with justification whether the area would then be increasing or decreasing.