solve all the part

Exercise 1: One-Dimensional Differential Calculus (20 Points) A firm's total costs of production are described by the following cost function: C(x) = =x3 + 2x3+ 10x+20. The firm's price-sales-function is given by p(x) = 8x + 10 a) Set up the profit function. (4P) b) Determine the extreme value(s) of the profit function (please do not forget to also check the sufficient condition). (10P) c) What is the maximum profit the firm can attain? (3P) d) Explain what is meant by the "inflection point" of the profit function. (3P)