First derivative as a direction test
Build sign diagrams for f′ and turn them into precise intervals of increase and decrease.
IB MATHEMATICS AA HL · TOPIC 5 · CALCULUS
Monotonicity & Concavity
A detailed standalone calculus chapter on increasing and decreasing functions, stationary points, first-derivative sign diagrams, first and second derivative tests, concavity, convexity and stationary or non-stationary points of inflexion. The pack also includes a separate worksheet and worked-solutions PDF.
HOW THE CHAPTER IS TAUGHT
Read the graph through the signs of its derivatives.
The notes connect the sign of f′ to direction and the sign of f″ to bending. Worked examples use sketches, sign charts, parameter problems, tangent and normal geometry, and longer original CF Maths synthesis questions so students learn to justify the shape rather than merely state it.
Classify stationary points properly
Use sign changes and second-derivative evidence without confusing stationary points with turning points.
Track how the gradient itself changes
Interpret f″ > 0 and f″ < 0 visually and algebraically.
Demand a change of concavity
Understand why f″(a)=0 alone is not enough, and distinguish stationary from non-stationary inflexions.
TOPIC 5 BUNDLE
Included in Topic 5 · Calculus · €50
The lecture notes, worksheet and worked solutions are included with the full current Calculus library.
Open the complete Topic 5 bundle →