Chapter Overview
The chapter 'Application of Derivatives' explores how the derivative of a function can be used in real-life and mathematical problem-solving. It emphasizes applications such as rate of change of quantities, determining monotonicity (increasing/decreasing nature), finding maxima and minima, and calculating tangents and normals to curves. These concepts are crucial in physics, economics, engineering, and daily problem-solving scenarios.
Important Keywords
- Rate of Change: Measures how a quantity changes with respect to another, often time.
- Increasing/Decreasing Functions: A function is increasing where its derivative is positive and decreasing where its derivative is negative.
- Tangent: A straight line that touches a curve at a point with the same slope.
- Normal: A line perpendicular to the tangent at a given point on the curve.
- Maxima and Minima: Points where a function reaches its highest or lowest value locally or globally.
- Point of Inflection: A point where the concavity of the function changes.
Detailed Notes
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