HSC Together Year 11 Maths Advanced: Gradient of a Secant as an Approximation of the Tangent

• Working With Functions
• Trigonometric Functions
• Calculus
• Exponential and Logarithmic Functions
• Statistical Analysis
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# Gradient of a Secant as an Approximation of the Tangent

### What is a secant?

In this post, we describe the gradient of a secant drawn through two nearby points on the graph of a continuous function as an approximation of the gradient of the tangent to the graph at those points, which improves in accuracy as the distance between the two points decreases. This is part of the Prelim Maths Advanced course under the topic Calculus and sub-part Gradients of Tangents. A secant is a line that intersects a curve at two or more points.

### Why do we use the gradient of a secant as an approximation of the tangent?

This video talks about the main reasoning and theory behind using the gradient of the secant to approximate the tangent.

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