A lab technician controls the temperature T inside a kiln. From an initial temperature of 0 degrees Celsius (°C), he allows the kiln to increase by 2°C per minute for the next 60 min. After the 60th minute, he allows the kiln to cool at the rate of 3°C per minute. The temperature function T is defined by
a) Find k such that T is continuous at t = 60.
b) Explain why T must be continuous at t = 60 min.