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Examples: Second Order Derivatives Video Lecture | Mathematics (Maths) for JEE Main & Advanced

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FAQs on Examples: Second Order Derivatives Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What is a second order derivative?
Ans. A second order derivative is the derivative of a derivative. It measures the rate of change of the rate of change of a function with respect to its independent variable.
2. How do you find the second order derivative of a function?
Ans. To find the second order derivative of a function, you need to differentiate the function twice. First, find the first derivative of the function and then differentiate it again to obtain the second order derivative.
3. What is the physical interpretation of a second order derivative?
Ans. The physical interpretation of a second order derivative depends on the context in which it is used. In physics, for example, the second order derivative of displacement with respect to time represents acceleration, which is the rate of change of velocity. In economics, the second order derivative of a production function represents the rate of change of the marginal product of labor, which indicates how the additional output changes due to a change in labor input.
4. Can the second order derivative be negative?
Ans. Yes, the second order derivative can be negative. A negative second order derivative indicates that the rate of change of the rate of change of a function is decreasing. This often occurs when the function is concave downward or has a maximum point.
5. What is the difference between the first and second order derivatives?
Ans. The first order derivative measures the rate of change of a function with respect to its independent variable. It represents the slope of the tangent line to the function at a given point. On the other hand, the second order derivative measures the rate of change of the rate of change of the function. It represents the curvature or concavity of the function at a given point.
209 videos|443 docs|143 tests

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