Compute the second derivative of standard function forms to analyse concavity.
Computes the second derivative f''(x) using the finite difference formula: f''(x) ≈ [f(x+h) − 2f(x) + f(x−h)] / h². The sign of f''(x) determines concavity: positive means concave up, negative means concave down, and zero may indicate an inflection point.
Second derivative (central difference)
f''(x) ≈ [f(x+h) - 2f(x) + f(x-h)] / h²
It measures the rate of change of the slope. Positive means the graph curves upward (concave up), negative means it curves downward (concave down).
Inflection points occur where f''(x) changes sign. Evaluate the second derivative at several points to find where it crosses zero.