Example 1

EXAMPLE 1: The side of a square increases at a rate of 3 cm/sec. Find the rate of change of the square’s perimeter and it’s area when the length of the side is 4 cm.

Solution: What rates are we trying to relate? What rates are given?

         Known:   ds/dt = 3 cm/sec    Unknown:     dP/dt = ?   dA/dt = ?

                                                                           when      s = 4 cm

Draw a sketch of the square and label the side, s. What equation relates s and P?

What equation relates s and A?


        P = 4s             A = s2

Now take the derivative of each of these equations with respect to time.