Cambridge O Level Additional Mathematics · Syllabus 4037 · Calculus
Second Derivative
What is Second Derivative?
The derivative of the first derivative, written f double dashed of x or d squared y by dx squared. It measures the rate at which the gradient itself is changing, so it describes how a curve bends: a positive second derivative means the gradient is increasing and the curve is concave upwards, and a negative second derivative means the gradient is decreasing and the curve is concave downwards. Its main use in Cambridge O Level Additional Mathematics 4037 is to classify a stationary point as a maximum or a minimum, and in kinematics it gives acceleration as the second derivative of displacement with respect to time.
This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.