All they want you to do here is choose one of the two lines x=4 and x=5.7 as delta. The one you choose is the one closest to x=5.

The reason being is that what you are saying is that when x is in between this line, f(x) is between the lines y=2.4 and y=3.6.

There's no math involved here. They wanted you to do this problem graphically. If they wanted you do do this analytically, they would have said so.