A man reading a newpaper walks at a constant speed away from the lamp which illuminates the paper he is reading.  The illumination from the lamp at clock time t is given by I = 30 / (t+3)², where I is illumination in watts/m² and t is clock time in seconds.

• At what average rate is the illumination from the lamp changing between clock times t = 4.5 and t = 4.6 seconds? 
• At what average rate is the illumination from the lamp changing between clock times t = 4.5 and t = 4.51 seconds? 
• At what average rate is the illumination from the lamp changing between clock times t = 4.5 and t = 4.501 seconds? 
• What do you estimate is the rate at which illumination is changing at clock time t = 4.5 seconds?

The rate at which the illumination a newspaper changes is given by Rate = 2610 / (t+3)³, where Rate is rate of change in watts/m² per second and t is clock time in seconds.  How much do you think illumination will change between t = 4.5 and t = 9 seconds?