For part "b", we will refer to the "rate of change" formula or for algebra also known as the "slope" formula:
\[m=\frac{ f(b)-f(a) }{ b-a }\]
The conditions for this is that (b-a) must not be equal to zero, because that would give an indetermined rate of change (some books call it infinite) and you can never have an infinite rate of change on a curve in this case.
So, with this, we can calculate the rate of change between two points, which in this case are (1,60) and (4,270) (the maximum point).
So, we will take "a" as the point (1,60), and "b" as the point (4,270) so therefore, f(a) is 60 and f(b) is 270, and "a" is equal to 1 and "b" is equal to 4, because they are values of "x" we choose.
So, let's now apply the slope formula for this two points:
\[m=\frac{ 270-60 }{ 4-1 }\]
And do the corresponding operations:
\[m=\frac{ 210 }{ 3 }\]
\[m=70\]
We can now conclude that the average rate of change is "70" but; What is this number?.
Well, this "70" in this specific function where x is the "price" and f(x) is the "profit", is called the "Marginal profit", and it represents the variation of the profit as we change the price of the unit.
Now, let's focus on the sign for a moment, and to make it more evident: We can observe that the m=70 does not have a "-" sign before it, so we can say that it is positive, so we can reprsent it as: m=+70.
This means that as we changes the price of the erasers from 1$ each to 4$ each we have an increase of profit, meaning that it is convenient for the Company to increase the price of the erasers to 4$.