(3) Suppose the total profit of a company at time to is P(t0) dollars and the profit is growing at the rate of PIUU) dollars per month. Which of the following best approximates the profit of the company at time :1 = 0 + At. i) P'(t1). ii) AP- iii) dP iv) ammo). 30 (b) The demand function for a brand of smoke alarm is given by (x) = 0 02 2 + 1 where x . :1: is the quantity demanded (in units of a thousand) and d is the unit price in dollars. Use differentials to estimate the change in the price when the quantity changes from 5000 to 5500 units. Show your work