Know the limits of numerical calculus

01

Press these keys

nDeriv(fnInt(GRAPHTABLE

02

Walkthrough

1
Inspect the function
Graph and table near the point for corners, holes, asymptotes or rapid oscillation.
2
Vary the view
Zoom and compare nearby inputs; numerical routines sample values and can miss structure.
3
Use mathematics
Check domain, continuity and analytic reasoning. Do not infer differentiability from one nDeriv output.

03

Worked example

Try nDeriv(|x|,x,0).

NORMAL FLOAT AUTO REAL MPa numerical value may appearleft slope −1, right slope +1

AnswerThe derivative at 0 does not exist despite any displayed approximation.