An AT cut crystal has a temperature vs. frequency characteristic that can be represented by a third order polynomial. The turning points are points of zero slope where the slope reverses sign. Usually there is a lower turning point around -4° C and an upper turning point around +55° C. Often ovenized oscillators hold the temperature of the crystal at the upper turning point to obtain maximum temperature stability.
In the growth cycles analysis, a turning point occur in a series when the deviation-from-trend series reached a local maximum (Peak) or a local minimum (Trough). Growth cycle peaks (end of expansion) occur when activity is furthest above its trend level. Growth cycle troughs (end of contraction/recession) occur when activity is furthest below its trend level.
a maximum or minimum point on a curve where the y-value changes from increasing to decreasing or vice versa (and the tangent is horizontal).