Mathematics (AS)·Differentiation · NSSCAS 1.8.3
Tangents, normals & rates of change
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Differentiation is not just a rule — it is a tool, and in this lesson you learn to use it. Miss Eve shows you the three-step recipe for the equation of a tangent, how to flip it into the normal, and how the sign of f′(x) tells you exactly where a curve rises and falls. Then you connect rates of change with the chain rule, and finish by finding a particle's velocity and acceleration from its displacement. By the end you can answer every classic 'tangent, normal, rate' exam question with confidence.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.8.3):
- Apply differentiation to find gradients of curves and the equations of tangents and normals at a given point.
- Apply differentiation to determine where a function is increasing and where it is decreasing.
- Apply differentiation to rates of change, including connected rates of change using dy/dt = dy/dx × dx/dt.
- Apply differentiation to motion problems: find velocity and acceleration from displacement, and interpret 'at rest' as v = 0.
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Miss Eve and Mike talk through the whole topic — with the figure and working drawn live.