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Second Order Derivatives Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Second Order Derivatives Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a second order derivative?
Ans. A second order derivative is the derivative of the derivative of a function. It measures the rate of change of the rate of change of a function at a specific point. It provides information about the curvature and concavity of the function.
2. How is the second order derivative calculated?
Ans. To calculate the second order derivative of a function, we need to take the derivative of the derivative. If the function is denoted as f(x), the second order derivative is written as f''(x) or d²f(x)/dx². It can be calculated by applying the derivative operator twice to the original function.
3. What does the second order derivative tell us about a function?
Ans. The second order derivative provides information about the shape and behavior of a function. It helps in determining the concavity of the function at a specific point. If the second order derivative is positive, the function is concave up, indicating a minimum point. If it is negative, the function is concave down, indicating a maximum point.
4. What is the physical interpretation of the second order derivative?
Ans. In physics, the second order derivative represents the acceleration of an object. It describes how the velocity of an object is changing with respect to time. If the second order derivative is positive, the object is accelerating in the positive direction. If it is negative, the object is decelerating or accelerating in the negative direction.
5. How can the second order derivative be used in optimization problems?
Ans. The second order derivative helps in optimizing functions by determining the critical points, such as maximum or minimum points. By analyzing the sign of the second order derivative at these critical points, we can determine whether they correspond to maximum or minimum values. This information is valuable in various fields, including economics, engineering, and physics, where optimization plays a crucial role.
204 videos|288 docs|139 tests

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