A stationary point on a curve is where the gradient is $0$, such as $(0, 0)$ on $x^2 + 5x$

The Local Maximum and Minimum

Building upon thi, there is local maximum and minimum points. These are both stationary, but also the highest/lowest points in the immediate vicinity.

$f'(x - h)$ and $f'(x + h)$ will not both be positive/negative.

Spelling

The plural of maximum is maxima. The plural of minimum is minima.

The Point of Inflection

Further more, there is the point of inflection, this is where the gradient is $0$ but $f'(x - h)$ and $f'(x + h)$ have are both positive/negative.

Comparison of Stationary Points