Cambridge O Level Additional Mathematics · Syllabus 4037 · Calculus
Second-Derivative Test
What is Second-Derivative Test?
A method of deciding whether a stationary point is a local maximum or a local minimum by evaluating the second derivative there. At a stationary value x equals a, if f double dashed of a is negative the curve is bending downwards and the point is a local maximum, and if f double dashed of a is positive the curve is bending upwards and the point is a local minimum. If f double dashed of a is zero the test gives no information and a different method must be used, such as examining the sign of the first derivative on either side of the stationary value. A complete justification states the stationary value, shows the second derivative evaluated at it, and draws the conclusion.
This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.