Second Derivatives
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) Text 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 d^{2}x/dx^{2}.
Demos
Second Derivatives
 
This demo graphs a function f(x) (in white) and its first and second derivatives (in green and red).

Exercises 1. Find the second derivative for each of the following functions, and check using the demo:
 f(x) = 0
 f(x) = 1
 f(x) = x
 f(x) = x + 5
 f(x) = x^{2}
 f(x) = x^{2} + 2x + 3
 f(x) = sin(x)
 f(x) = cos(2x)
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)?
