Suppose that the revenue and cost functions for a firm are given as follows

TR = 70q - q²

TC = q² + 30q + 100

a. Find the quantity that maximizes profit. (find q that's at the top of the mountain)

b. Verify that the q you've found in a. is a max; rather than a min. (2nd order condition).

Notes: Profit = Total Revenue - Total Cost. Show all steps in your calculations.