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The derivative of digital function is defined in terms of difference. Then, which of the following defines the second order derivative ∂2 f/∂x2 = ___________ of a one-dimensional function f(x)?

The derivative of digital function is defined in terms of difference. Then, which of the following defines the second order derivative ∂2 f/∂x2 = ___________ of a one-dimensional function f(x)? Correct Answer f(x+1)+ f(x-1)-2f(x)

The definition of a second order derivative of a one dimensional image f(x) is: (∂2 f)/∂x2 =f(x+1)+ f(x-1)-2f(x), where the partial derivative is used to keep notation same even for f(x, y) when partial derivative will be dealt along two spatial axes.

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What kind of relation can be obtained between first order derivative and second order derivative of an image having a on the basis of edge productions that shows a transition like a ramp of constant slope?
What kind of relation can be obtained between first order derivative and second order derivative of an image on the response obtained by encountering an isolated noise point in the image?
What kind of relation can be obtained between the response of first order derivative and second order derivative of an image having a transition into gray-level step from zero?
Assertion (A): It is observed that step function is first derivative of a ramp function and impulse function is first derivative of a step function. Reason (R): From the derived time response expression it is concluded that the output time response also follows the same sequence as that of input functions.