The derivative of a variable y with respect to x is defined as the ratio between the change in y and the change in x, depending upon the condition that changes in x should be very small, tending towards zero.
The application of derivatives (from calculus) centers on using the derivative to analyze how a quantity changes with respect to another.
Derivatives are crucial in mathematics and have wide applications in fields like engineering, architecture, economics, and more. They help in understanding how physical quantities change, such as velocity (rate of change of displacement) and acceleration (rate of change of velocity).
Real-Life Examples:
- A carâs speed at a specific moment is the rate of change of its position with respect to time.
- An engineer designs a container to maximize volume with minimum material.
- A shopkeeper estimates cost change for a slight price increase.
Foundations
Covers the basic concepts required for applications of derivatives.
Rate of Change
Understanding how quantities vary with respect to each other.
Tangents and Normals
Equations related to curves at a point.
Increaing and Decreasing
Analyzing behavior of functions using derivatives.
Maxima and Minima
Finding maximum and minimum values of functions.
- Local Maxima and Minima
- Absolute Maxima and Minima
- First Derivative Test
- Second Derivative Test
- Maxima and Minima
Approximation
Using derivatives for estimation.
Practice
Evaluate learning and test your understanding with some practice and quizzes.
