AP Calculus AB: Concavity and Second Derivative Test — Drill 1

About This Drill

AP Calculus AB: Concavity and Second Derivative Test — Drill 1 is a Math practice drill covering Concavity and Second Derivative Test. 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 second derivative to determine concavity, identify points of inflection, and apply the Second Derivative Test to classify relative extrema. These AP Calculus AB skills are essential for curve analysis on the AP exam.

Questions in This Drill

1. Let \( f(x) = x^4 - 4x^3 \). On which of the following intervals is the graph of \( f \) concave up?
2. Let \( f(x) = x^3 - 3x^2 + 4 \). At which value of \( x \) does \( f \) have a point of inflection?
3. Let \( f(x) = x^4 - 8x^2 \). Which of the following correctly classifies the critical point at \( x = 2 \)?
4. For a twice-differentiable function \( g \), it is known that \( g''(4) = 0 \). Which of the following must be true?
5. A particle moves along a straight line with velocity \( v(t) \) for \( t \geq 0 \). It is given that \( v(t) > 0 \), \( v'(t) > 0 \), and \( v''(t) < 0 \) for all \( t \) in the interval \( (0, 5) \). Which of the following correctly describes the particle’s motion on \( (0, 5) \)?