Calculus
Intermediate

Second Derivative Test

Concavity determines local minima and maxima.

Formula

f′′(x)>0⇒minf''(x) > 0 \Rightarrow \text{min}

Variables

f''Second derivative

Example

Positive = concave up = minimum

Did You Know?

The second derivative measures acceleration and reveals whether a curve is concave up or down.

optimization