Question

Question 4 (13 marks) You just bought 10,000 shares of a given stock at the price of x dollars per share. Some researches showed that the rate of loss f (in %) on the stock in one year after bought at price x is given as follows: Ax-3 if x < 2 f(x) = 13-x+ 2x2 if x 22 a) What value(s) of A can make the function (x) continuous for all x. (9 marks) b) For the above-determined A, find the range for buying price x that can lead to a positive return in one year. (4 marks)

Answer 1

for f(x) to continuous f(x)=(Ax-3 x<2 3-2 +2e? 272 - for both is polynomial continuous in domain or defined a, but continuous at x=2, both piece of function value must be equal I f(2)= lim f(x)= lim fix) - 2 x 2" - 3-2 +2.2² lim (2-2)A-3)=lim (3-12th) +2.12th hoo - 9 = 2A-3 = 1+ 8 A = +3=6 A=67 (b) for positive return rate of loss must be negative 6x- 3co xa ž. a losxat it's negative so (-) rate - of loss and positive return. Range is oto 0.5 6x-3{0<x<2) 3-x-2x{ 2} (2.9) 6080 shown ingroph as well. (05,0) (0.-3)

!! PLEASE VOTE WITH MANY THUMBS UP !!