How a tangent line can predict the path of a curve
In short: This video demonstrates how to use local linearity to estimate function values. By finding a tangent line's equation via the derivative, you can approximate nearby x-values on a curve.
The lesson explores the concept of local linearity, where a curve behaves like a straight line when viewed closely. By calculating the derivative at a specific point, you can determine the equation of the tangent line at that location.
Once the tangent line is established, it serves as a tool to approximate the function's value for x-values near the original point. This technique is a fundamental concept in AP Calculus AB.
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Sources
- Summary by Intellect · source: Worked example: Approximation with local linearity | AP Calculus AB | Khan Academy
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