Question

We know that first order differentiation of a function is a tangent to graph. My question is :-
'How can one show the second order derivative/second order differentiation on a graph ?'

Answer 1

The first derivative gives us the slope of the graph at a given point.
The 2nd derivative tells us if the graph is concave up or concave down at a given point.

Answer 2

If you're gonna graph the 2nd derivative, you want to cross the x-axis wherever there is an inflection point (when if switches from concave up to concave down or vice versa). Obviously make sure you're above the x-axis whenever your function is concave up and below the x-axis whenever your graph is concave down.

Answer 3

@BangkokGarrett What you will say about much higher derivatives ?

Answer 4

I believe higher derivatives are more difficult to see visually.
The 3rd order is how fast the concavity is changinging.
The 4th order is how fast the change in the concavity is changing.
The 5th order is how fast the change in the change in the concavity is changing.
etc....