Derivatives and Marginal Analysis

Question

The R.C. Helliot Advertising Company finds that its profits on day  of an advertising campaign is given by where  is profit in dollars for day of the campaign.

1.What is the exact rate of change of profits when 35 days have been passed in the campaign? The rate of change is Incorrect dollars per day. (Your answer may be negative.)

2.What are their total profits on day 35 of the campaign?Total profits on day 35 are? 

Answer 1

take the derivative to find the marginal profit

P'(t) = -5t+40

P'(35) =-5(35)+40 =-175+40 = -$135 per day

= the instantaneous rate of change on day 35

P(35) =-2.5(35)^2 +40(35) + 44,000

=-3062.5 + 700 + 44,000

= $41,637.50 = total profits on day 35