solution:
The closing price (in dollars) per share of stock of Tempco Electronics on the tth day it was
traded is approximated by
P(t) = 20 + 12 sin πt/30 − 6 sin πt/15 + 4 sin πt/10 − 3 sin 2πt/15 (0 ≤ t ≤ 24)
where t = 0 corresponds to the time the stock was first listed on a major stock exchange.
What was the rate of change of the stock's price at the close of the 15th day of trading?
P'(t) = 12(cos πt/30) - 6 (cos πt/15) + 4(cos πt/10) - 3(cos 2πt/15)
t = 15
P'(t) = 12(cos 15π/30) - 6 (cos 15π/15) + 4(cos 15π/10) - 3(cos 30π/15)
P'(t) = 12(cos π/2) - 6 (cos π) + 4(cos 3π/2) - 3(cos 2π)
P'(t) = 12(0) - 6(-1) + 4(0) - 3(1) = 6 - 3
P'(t) = $3 per day RATE OF CHANGE
the closing price on that day
P(t) = 20 + 12 sin πt/30 − 6 sin πt/15 + 4 sin πt/10 − 3 sin 2πt/15
t = 15
P(t) = 20 + 12 sin 15π/30 − 6 sin 15π/15 + 4 sin 15π/10 − 3 sin 30πt/15
P(t) = 20 + 12 sin π/2 − 6 sin π + 4 sin 3π/2 − 3 sin 2π
P(t) = 20 + 12(1) − 6(0) + 4(-1) − 3(0) = 20 + 12 - 0 - 4 - 0 = 20 + 12 - 4
P(t) = $28 per share close price
