Points of Inflection (Edexcel A-Level Mathematics): Flashcards

It's where the graph changes concavity.

$f''(c)$ must equal zero or be undefined at $c$.

The second derivative changes sign at $x = c$.

Solve $f''(x) = 0$ for $x$.

$f''(x)$ changes sign around $x = c$.

Set $f''(x) = 0$; find changes in concavity.

$f''(x) > 0$.

$f''(x) < 0$.

Graph changes from concave up to down, or vice versa.

Derivative is zero; concavity changes at this point.