Read the result
The first derivative compares the two side values. The second derivative measures how far the centre value sits from their average.
Numerical differentiation
Central Difference Derivative Lab
Estimate first and second derivatives from values on both sides of a point.
Formula
f'(a) approx (f(a+h)-f(a-h))/(2h), f''(a) approx (f(a+h)-2f(a)+f(a-h))/h^2
Result
Worked substitution
Central differences cancel more error than one-sided differences, but tiny h can amplify rounding noise.
Where it helps
Use it when you have measured or tabulated values rather than a clean formula.
Common slip
A smaller h is not always better; subtracting nearly equal rounded values can damage accuracy.
Try it
Halve all three x-spacings conceptually by changing h and see how strongly the estimates respond.