Financial analysts use graphical models to predict stock values for a new stock. It is important for stock brokers to know about instantaneous changes of a stock price. To make a stock pricing model, analysts look at past behavior and future expectations for that stock. A stock broker has developed the following model for the price of his favourite stock:

() = { 2 2 + + , < 0

, = 0

3( + 1) 4 + , > 0

a) Why is it important for the stock broker to know about the instantaneous changes of a stock price?

b) What should be true about the function f(t) in order for the stock broker to know how fast the stock price is changing in the present instant (t=0).

c) Determine the values of a, b and c that make the function f(t) differentiable at t=0. [2A] d) Determine algebraically the instantaneous rate of change at this present instant (t=0)

d)Determine algebraically the instantaneous rate of change at this present instant (t=0)

e) Make a sketch of f(t).