I want the detailed solution for part "d" and part "e" only. And, For part "D" = The answer should be in between $500,000 to $600,000. For part "E" = The answer should be in between $700,000 to $800,000.

It turns out that you would like to take some risk and decide to invest $100,000 into the stock market. Utilising the data science knowledge learned at Monash, you did some research and get to know the price of a stock is given by a function f(t)=(t1)3(20t3104t2+143t19)+30, accurately for all 0t3. (a) Compute the derivative f(t) and find all stationary points of f. (b) On which intervals in t[0,3] is f(t) increasing, and where is it decreasing? Classify all stationary points of f as a local minimum, local maximum or neither. (c) Find the global minimum and the global maximum of f. (d) Assume that the family is cautious so you buy shares only once and sell shares only once. How much money you can make by the end of the third year? (e) How much money you can make by buying/selling shares several times