Learn how to find the equation of a tangent line to a curve – one of the most common applications of derivatives. I present the theory and several different types of example.

Key Points

A tangent line meets a curve at a single point, the point of tangency

A tangent line is a ‘line’ so we find it’s equation using y – b = m (x – a)

To use y – b = m (x – a) we need the gradient, m, and a point on the line, (a,b)

(a,b) will be the point of tangency

The gradient, m, we find by taking the derivative and evaluating at x = a

In other words, m = f ‘(a)

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