the solution of question 12 and 13

12. (5 points) Suppose the total profit (in thousands of dollars) from selling r kilograms of a certain product is given by P(x) = --x'+2x3+ 3x2 +5x -4 It turns out that the function P has only one critical number c > 0. (a) Find the number of kilograms, to the nearest hundredth, that should be sold in order to maximize the total profit. (b) What is the maximum profit? 13. (5 points) Consider the equation 1 + In(x - 2) = 0. (a) Find the exact solution. Then find an approximate solution (round your answer to two decimal places). (b) If the initial guess is c1 = 2.1, use Newton's method to approximate the solution to the nearest hundredth. Compare your answer to the one found in part (a). (c) Explain why Newton's method does not work if the initial guess is c1 = 3