verbatim: Wiki Wednesday

Time to learn something!

1. Go to Wikipedia.
2. Click on "Random article" in the left-hand sidebar box.
3. Post it!

Here's what I got:

In mathematics, the higher-order derivative test is used to find maxima, minima, and points of inflection in an n^th degree polynomial's curve.

Let $f$ be a differentiable function on the interval $I$ and let $c$ be a point on it such that

$f'(c)=f''(c)=f'''(c)=\cdots=f^{n-1}(c)=0$ ;

$f (n) (c)$ exists and is non-zero.

Then,

if n is even
$f^n(x)<0 \implies x=c$ is a point of local maximum

$f^n(x)>0 \implies x=c$ is a point of local minimum

if n is odd $\implies x=c$ is a point of inflection