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:

                               .



At what point does the function have a local minimum (the first question) resp. maximum (the second
question)?

At what point does the function have a local minimum?


At how many points does the function g have a local minimum and the function f a local maximum?