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vikcool812
- 13
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If x and y are defined in terms of a third vatiable say t , then to find d2y/dx2 , we cannot find d2y/dt2 and d2x/dt2 and divide them to get d2y/dx2 , i am unable to fingure out the reason for this !
The second derivative is a mathematical concept that describes the rate of change of a function's slope. It is the derivative of the derivative of the original function.
To find the second derivative from parametric form, you first calculate the first derivative of the parametric equations for both x and y. Then, you take the derivative of the first derivatives with respect to the parameter. This will give you the second derivative for both x and y, which can be written as a vector.
The second derivative provides information about the curvature of a function. It can help determine if a function is concave or convex, and can be used to find inflection points. It is also useful in optimization problems, where finding the maximum or minimum of a function is desired.
Yes, the second derivative can be negative. This indicates a concave down curvature, which means the function is decreasing at an increasing rate. Conversely, a positive second derivative indicates a concave up curvature, where the function is increasing at an increasing rate.
No, the second derivative may not exist for some functions, such as those with sharp corners or discontinuities. In these cases, the function is said to be non-differentiable at that point and the second derivative cannot be calculated.