The revenue agency outlines the following tax schedule: If a person earns up to $2000, then he is taxed at 5%. The next $10,000 will be taxed at 10%. Any additional income is taxed at 25%. Let T denote tax, and I denote income. 

a) Derive Marginal Tax Function and draw the corresponding graph.

b) Derive Tax Function and draw the corresponding graph.

c) Show that the marginal tax function is not continuous at I=2000..

d) Show that the tax function is continuous at I=2000, but not differentiable.