At \(P(a,f(a))\), the derivative \(f'(a)\) is the gradient of the tangent. Always find the point as well as the gradient.

Translate the geometry into a derivative condition: parallel lines have equal gradients; two perpendicular non-vertical lines satisfy \(m_1m_2=-1\). Combine this with the curve equation and any given coordinates.

Paper 1: keep exact values and show algebra. Papers 2 and 3: record the equation you solve, use the required domain and give the requested accuracy.

Applications of Differentiation

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Tangents and Normals

Tangents and Normals