AASL 5.8.1 Classifying stationary points

In this lesson, the process of classifying stationary points is explained, focusing on determining whether a point is a maximum, minimum, or a point of inflection. A stationary point occurs where the first derivative equals zero, denoted as $\frac{dy}{dx} = 0$.

To find stationary points, the first derivative of the function is calculated, leading to the equation . The solution yields the stationary point at . The classification of this point is achieved by evaluating the ; if it is greater than zero, the point is a minimum, while if it is less than zero, it is a maximum. If the second derivative equals zero, further analysis is required, such as using a sign chart to determine the nature of the stationary point.