After a new version of a certain type of computer is released, the total worldwide profits (in billions of dollars) are approximated by the function 135t2 + 130t P(t) = t2 + 2t + 1 ,t20 where t is measured in years after the computer's release. a) Find P'(t) using differentiation rules (by hand). b) Use Geogebra CAS to verify your answer in (a): . Define the function P(t) by inputting P(t) = if (t>=0, 135t2+130t ). 12 + 2t+1 . Find the derivative of P(t) by inputting P' (t). C) How fast is the profit changing a year after the computer's release? d) What will the total profit be at that time? e) What is lim P(t) and lim P'(t)? Explain what they mean in this situation. 1-+00 1-+00