Q: What is the practical meaning of second derivative?

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The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

Yes.

No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6

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The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.

The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.

All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2

well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

2x is the first derivative of x2.

2x is the first derivative of x2.

Yes.

Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)

the second derivative at an inflectiion point is zero

No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6

The same way you get the second derivative from any function. Assuming you have a function that expresses potential energy as a function of time, or perhaps as a function of position, you take the derivate of this function. This will give you another function. Then, you take the derivate of this derivative, to get the second derivative.

d/dx(X^4) = 4X^3 ( first derivative ) d/dx(4X^3) = 12X^2 ( second derivative )