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The second derivative of a function is the derivative of the derivative.
For a function f(x), the second derivative is written either as f ''(x) or as d2x/dx2.
This demo graphs a function f(x) (in white) and its first and second derivatives (in green and red).
Exercises1. Find the second derivative for each of the following functions, and check using the demo:
2. Try various polynomial functions for f(x). How do the degrees of f '(x) and f ''(x) relate to the degree of f(x)?
- f(x) = 0
- f(x) = 1
- f(x) = x
- f(x) = x + 5
- f(x) = x2
- f(x) = x2 + 2x + 3
- f(x) = sin(x)
- f(x) = cos(2x)