Home › AP Calculus AB › Mathematics › Applications of Derivatives › Checking concavity through the sign of the secon…
Checking concavity through the sign of the second derivative is known as the:
AConcavity test
BContinuity test
CConvergence test
DComparison test
Answer & Solution
Correct answer: A. Concavity test
1. A positive second derivative means the slope is rising.
2. A negative one means the slope is falling.
3. Using that sign is the concavity test.
_Source: OpenStax Calculus Volume 1, Chapter 4, Applications of Derivatives._
Related questions
A tank is draining and a student is asked how fast the depth falls when the volume is chanThe notation used for a family of antiderivatives, complete with its constant, is the:Knowing an object's velocity, a student recovers its position by finding an:A function whose derivative is the given function is called its:Calculators and computers rely on that same tangent-based idea when they find:An iterative technique for finding zeroes, built on tangent line approximations, is:The rule that resolves such a limit by differentiating numerator and denominator separatelA limit produces the form zero over zero, so its behaviour cannot be read off directly. Th