A manufacturer of lightbulbs wants to produce bulbs that last about 700 hours but, of course, some bulbs burn out faster than others. Let F (t) be the fraction of the company’s bulbs that burn out before hours, so F (t) always lies between 0 and 1.
(a) Make a rough sketch of what you think the graph of F might look like.
(b) What is the meaning of the derivative r (t) = F’ (t)?
(c) What is the value of ∫∞ r (t)? Why?