Mathematics (AS)·Differentiation · NSSCAS 1.8.4
Stationary points
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Every curve has special spots where it stops climbing or falling for a moment — those are stationary points, and they win marks in almost every NSSCAS paper. In this lesson you will learn to locate them by solving f′(x) = 0, and to classify each one as a maximum, a minimum or a point of inflexion. You will master two classification tools: the quick second-derivative test and the trusty gradient sign table. We finish by using calculus to help a Namibian farmer fence the biggest possible camp. By the end, you will handle even the sneaky cases examiners love.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.8.4):
- Locate stationary points on a curve by solving f′(x) = 0 and finding the matching y-coordinates.
- Distinguish between maximum points, minimum points and stationary points of inflexion using both the second-derivative test and a gradient sign table.
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