Pure · Differentiation
Chapter 1 · 3
The idea
Convex, concave and points of inflection
Using the second derivative to decide where a curve is convex (f'' > 0) or concave (f'' < 0), and locating points of inflection where the concavity changes — distinct from a stationary point.
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Pure · Differentiation
Convex, concave and points of inflection
Using the second derivative to decide where a curve is convex (f'' > 0) or concave (f'' < 0), and locating points of inflection where the concavity changes — distinct from a stationary point.
Why it works
Which way it bends
The first derivative tells you whether a curve is going up or down. The second derivative tells you which way it bends — and that shape information is what this section is about.- Where the gradient is increasing, so the curve bends upward like a valley: it is convex (often said "concave up"). It sits above its tangents.
- Where the gradient is decreasing, so the curve bends downward like a hill: it is concave (or "concave down"). It sits below its tangents.
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