Portrait of Maria Gaetana Agnesi

Maria Gaetana Agnesi, an 18th-century Italian mathematician, famous for "the witch of Agnesi", decided to buy a new pendulum clock. Maria Gaetana Agnesi, an 18th century Italian mathematician, well known for the "Agnesi curve", is mainly known in the area of analysis, with the publication of the first complete book on Differential and Integral Calculus.

Let us suppose the situation in which Maria Gaetana Agnesi had to help a friend of hers who was a watch seller".

 Read carefully and try to answer the questions:

The clock seller, a friend of Maria, told her about her finances: "Now, my monthly income is €50 for each clock I sell, but the company has suggested a new approach and given me the following conditions: €300 fixed euros a month and €20 commission for each clock I sell. Maria, as an extraordinary mathematician, can you help me decide what's best for me?".

Help both friends by answering the following questions:

a) Find the functions that connect the number of clocks sold with the monthly income in each situation.

d) What are the kind of functions obtained?

c) Draw their graphical representation on the same axes.

d) If you were the seller, would you accept the new conditions? Give reasons for your answer.