4.25 Summary (Remember these!)

Maclaurin’s formula

On the graph of $f$,

$f^{\prime}(x)>0$ gives $f$ increasing;

$f^{\prime}(x)<0$ gives $f$ decreasing;

$f^{\prime}(x)=0$ gives a stationary point.

At a stationary point $a$,

$f^{\prime\prime}(a)>0$ gives a local minimum;

$f^{\prime\prime}(a)<0$ gives a local maximum.