Work on intervals within the domain. The height of the derivative graph gives the gradient of the original curve.

Solve \(f'(x)=0\) and identify points where the function or derivative is undefined.

Split the domain at these values and test the sign of the derivative on each interval.

State intervals clearly, excluding points outside the domain.

An isolated zero derivative need not interrupt increase: \(f(x)=x^3\) increases across \(x=0\), although \(f'(0)=0\). Use the sign on either side, not just the value at one point.

Increasing and Decreasing Functions

Differentiation

International Baccalaureate Mathematics: Analysis and Approaches Higher Level