Mathematics in Economics – lecture 4 1) Extreme of function The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and A) the second derivative is positive at this point, then f has a local minimum here. B) the second derivative is negative at this point, then f has a local maximum here. Find the maximum of total revenue function . Find the minimum of total cost function: . Find the maximum of the profit function: . Find the maximum of total revenue function: .