Differentiation, a fundamental concept in calculus, has numerous applications in various fields of study. Here are some of the key applications:
- Determining the Rate of Change of a Quantity
- Evaluating Increasing and Decreasing Functions
- Drawing Tangent and Normal to a Curve
- Finding Minimum and Maximum Values
- Implementing Newton’s Method
- Making Linear Approximations
In this discussion, we will delve into one of the most essential applications of differentiation: tangents and normals.
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A tangent is a line that just touches the curve at a single point, while the normal is a line that is perpendicular to the tangent at that point.
Let's use differentiation to derive the equations of the tangent line and the normal line to a curve at a specified point.