Learn how to find the equation of a tangent line to a curve.
One of the first applications of derivatives that students learn is how to find the equation of a tangent to a curve. There are many applications of derivatives but this one is particularly important. It was actually from trying to solve the tangent line problem that Mathematicians in the 1600’s developed Calculus techniques. History aside, all differentiation students should be prepared to demonstrate how to find the equation of a tangent line to a curve as it’s a very common exam question type. Any questions about this video drop us a message HERE.
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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