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

Q: What is the geometrical 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.

point is also known as dot.

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.

The partial derivative of z=f(x,y) have a simple geometrical representation. Suppose the graph of z = f (x y) is the surface shown. Consider the partial derivative of f with respect to x at a point. Holding y constant and varying x, we trace out a curve that is the intersection of the surface with the vertical plane. The partial derivative measures the change in z per unit increase in x along this curve. Thus, it is just the slope of the curve at a value of x. The geometrical interpretation of is analogous in both types of derivatives, i.e., Ordinary and Partial Derivatives

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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.

point is also known as dot.

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)

To get the second derivative of potential energy, you first need to calculate the first derivative of potential energy with respect to the variable of interest. Then, you calculate the derivative of this expression. This second derivative gives you the rate of change of the slope of the potential energy curve, providing insight into the curvature of the potential energy surface.

The partial derivative of z=f(x,y) have a simple geometrical representation. Suppose the graph of z = f (x y) is the surface shown. Consider the partial derivative of f with respect to x at a point. Holding y constant and varying x, we trace out a curve that is the intersection of the surface with the vertical plane. The partial derivative measures the change in z per unit increase in x along this curve. Thus, it is just the slope of the curve at a value of x. The geometrical interpretation of is analogous in both types of derivatives, i.e., Ordinary and Partial Derivatives

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