Compute the third derivative of standard function forms for jerk analysis.
Computes the third derivative f'''(x) using the finite difference formula: f'''(x) ≈ [f(x+2h) − 2f(x+h) + 2f(x−h) − f(x−2h)] / (2h³). In physics, the third derivative of position with respect to time is called jerk.
Third derivative
f'''(x) ≈ [f(x+2h) - 2f(x+h) + 2f(x-h) - f(x-2h)] / (2h³)
In kinematics, it represents jerk — the rate of change of acceleration. It's important in engineering for ride comfort analysis.
Higher-order finite differences amplify numerical noise, so a slightly larger h balances truncation error against round-off error.