It is projected that t months from now,the average price per unit for goods in a certain sector of the economy will be P(t) = -t^3 + 7t^2 + 200t + 300 dollars.
a.) At what rate will the price increase be changing with respect to time 5 months from now?
ANSWER: P'(t) = -3t^2 + 14t + 200 so P'(5) = 195
b.) At what rate will the rate of price increase be changing with respect to time 5 months from now?
ANSWER: P"(t) = -6t + 14 so P"(5) = -16
c.) Use calculus to estimate the change in the rate of price increase during the first half of the sixth month.
Doubting ANSWER: -16 * (3/2) = -24
d.) Compute the actual change in the rate of price increase during the first half of the sixth month.
Doubting ANSWER: P'(-24) - P'(5)
P'(-24) = -3*(-24)^2 + 14*(-24) + 200
P'(-24) = -1756 - 336 + 200
P'(-24) = -2059
P'(-5) = -3*(-5)^2 + 14*(-5) + 200
P'(-5) = -75 -70 + 200
P'(-5) = 55
-2059 - 55 = 2114
I know that part d is way off base and I would appreciate your help.