Math basics › Calculus
Using derivatives
Critical points
Where f′ = 0 or is undefined. Maxima and minima can only happen there.
First derivative test
f′ changing + to − is a maximum, − to + is a minimum. No change means neither.
Second derivative
f″ > 0 is concave up, f″ < 0 is concave down. Where it changes sign is an inflection point.