AP Calculus AB: Definition of the Derivative — Drill 1

About This Drill

AP Calculus AB: Definition of the Derivative — Drill 1 is a Math practice drill covering Definition of the Derivative. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice using the limit definition of the derivative and interpreting derivatives as instantaneous rates of change. These AP Calculus AB skills appear on both the multiple-choice and free-response sections.

Questions in This Drill

1. If \( f(x) = x^2 + 3x \), which of the following correctly expresses \( f'(x) \) using the limit definition of the derivative?
2. Using the limit definition of the derivative, what is \( f'(2) \) if \( f(x) = 3x^2 \)?
3. The table below shows selected values of a function \( g \).
   
   

   x	1	3	5	7
   g(x)	4	10	18	24

   
   Which of the following is the best estimate for \( g'(5) \)?
4. A company's revenue (in thousands of dollars) \( t \) months after launch is modeled by a differentiable function \( R(t) \). It is given that \( R(6) = 85 \) and \( R'(6) = 4.2 \). Which of the following best interprets \( R'(6) = 4.2 \)?
5. Which of the following limits equals \( f'(5) \) if \( f(x) = \sqrt{x} \)?