#### To determine

**(a)**

**To interpret:**

Meaning of f'r and its units.

#### Answer

f'r denotes rate of change of cost of students loan with respect to interest rate. Its units are dollars/ (percent per year)

#### Explanation

**1) Given:**

The total cost function C=fr, where r is interest rate of loan given in percent.

**2) Calculations:**

Total cost C =fr, where interest rate of loan is r%.

Derivative represent the rate of change.

Therefore, f'r denote rate of change of cost of students’ loan with respect to interest rate.

Since the unit of C is dollars and unit of r is percent per year, the required unit is dollars / percent per year.

**Final statement:**

f'r denote rate of change of cost of students’ loan with respect to interest rate. Its units are dollars/ (percent per year)

#### To determine

**(b)**

**To interpret: **Meaning of f'10=1200.

#### Answer

**Answer: f'10=1200**means at 10% interest rate, cost of repaying of student loan increases by 1200 dollars per interest per year. Means if interest rate goes up from 10% to 11%, the cost goes up approximately by $1200.

#### Explanation

**1) Given:**

The total cost function C=fr, where r is interest rate of loan given in percent and f'10=1200.

**2) Concept:**

As f'r denote rate of change of cost of student loan with respect to change in interest rate.f'10=1200 means at 10% interest rate, cost of repaying of student loan increases by 1200 dollar per interest per year. In other words, if interest rate goes up from 10% to 11%, the cost goes up approximately $1200.

**Final statement:**

f'10=1200 means at 10% interest rate, cost of repaying of student loan increases by 1200 dollar per interest per year. Means if interest rate goes up from 10% to 11%, the cost goes up approximately $1200.

#### To determine

**(c)**

**To check: f'r**always positive or not.

#### Answer

**Answer: f'r**is always positive.

#### Explanation

**1) Given:**

The total cost function C=fr, where r is interest rate of loan.

**2) Concept:**

As rate of interest increases cost of repaying of student loan also increases. Therefore, f'r is always positive.

**Final statement:**

As r increases, C increases. So f'r is always positive.