Question 1 Given the function f (x) = 3x-9 a) Find f(6), b) Define the domain and range. c) Find the limit of f(x) as x approaches infinity. Question 2 In 2016 an investor invests 400.000 euros in a scheme which promises a 2% return each year, but in 2019 finds a better option and takes all of his previous Investment and it's return and puts it somewhere which promises 3.5% return each year. How much money will they have in 2022 assuming both investments returned the promised amount. Question 3 Differentiate the following functions. a) f(x) = 6x5 -4x2+1 b) f (x) =# + v x-5x c) f (x ) = (x2 + 4x)4 Question 4 A company's profit function, given in millions of euros, is defined as p(x) = - x2 20 X2 + 4x,. Find, by differentiation, the marginal profit function and hence which value of x maximises the profit, and what the maximum profit is. Question 5 Evaluate the following integrals: a) [9x2 + 4x - 3 dx b) [ 6x2 (2x3 + 3)5 dx You can use substitution u = 2x3 + 3 c) So x2 - 6 dx Question 6 A start-up's marginal revenue function, in millions of euros, is given by r'(t) = at +, where t is measured in years. Using a definite integral, calculate how much revenue the company produced in the first 3 years