Analysis of daily output by a factory employee shows that, onaverage, the number of units per hour produced after t hours on thejob can be modeled by y = 70t + 0.5t 2 − t 3 where 0 ≤ t ≤ 8.
(a) Thinking about the context of this problem, explain whyt-values in this model might be restricted to values between t = 0and t = 8.
(b) Find all the critical numbers for this function. Hint: Youmay want to use the quadratic formula or a quadratic program onyour calculator as part of this calculation.
(c) Which critical number(s) that you found in part (b) makesense in this problem? Explain your reasoning in the context ofthis problem.
(d) For the critical number(s) you stated in part (c), explain,in the context of this problem, what this critical number tellsyou.
