MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A rectangle has length x(t) cm and width y(t) cm, both varying with time t.
Answer the following questions neatly showing all steps.
(i) Write the formula for the perimeter P(t) of the rectangle in terms of x(t) and y(t).
(ii) Differentiate your expression in part (i) with respect to t and obtain a relation between dP/dt, dx/dt and dy/dt.
(iii) At a certain instant the length is increasing at 2cm s−1 while the width is decreasing at 2cm s−1. State, with reason, whether the perimeter is increasing, decreasing or remaining constant at that instant.
(iv) Derive the general condition connecting dx/dt and dy/dt for which the perimeter of the rectangle does not change with time.