The Second Derivative

Differentiation III

In this course, Professor Samir Siksek (University of Warwick) concludes his discussion of differentiation for A-Level students in the third of this three-course series. In the first mini-lecture, we introduce the second derivative and work through some examples. In the second mini-lecture, we explore the relationship between the first and second derivative as well as the relationship between the second derivative and stationary points (local maxima and local minima). In the third mini-lecture, we learn how to classify stationary points as a local maximum, local minimum, or point of infection. In the fourth mini-lecture, we introduce the chain rule as a way to differentiate compositions of functions.

The Second Derivative

In this mini-lecture, we introduce the second derivative, focusing in particular on: (i) using the notation dy/dx as an alternate way to write the first derivative f′(x); (ii) the notation d²x/dx² to denote the second derivative, which is computed by differentiation the function twice; and (iii) some examples and exercises on computing the second derivative.