Name: AASL 5.4 Tangents and normals
Uploaded: 2025-01-04T10:03:14.160Z
Duration: 9 min 49 s
Description: Learn AASL 5.4 Tangents and normals in this free IB Mathematics Analysis and Approaches (AA) video lesson for SL 5.4—Tangents and normal.

In this lesson, the process of finding the equations of the tangent and normal lines to a curve is explained, emphasizing the connection between tangents and derivatives. The tangent line touches the curve at a single point without crossing it, while the normal line is perpendicular to the tangent.

To find these equations, the following steps are outlined:

Identify a point on the curve, which is determined by substituting the given x-coordinate into the function.
Calculate the gradient using the derivative of the function, where the derivative at a point gives the slope of the tangent line.
Use the formula $y - y_1 = m(x - x_1)$ to derive the equations for both the tangent and normal lines, noting that the gradient of the normal is the negative reciprocal of the tangent's gradient.

The final equations are presented in different forms for clarity, demonstrating the versatility of the approach.

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