turning point / inflection point
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turning point
A point in time at which a decisive change occurs in a development or course of events, fundamentally changing its direction.
Die Erfindung des Internets war ein Wendepunkt in der Geschichte der Kommunikation.
The invention of the internet was a turning point in the history of communication.
'Wendepunkt' is made up of 'Wende' (turn, change) and 'Punkt' (point). So it literally describes a point at which a decisive turn takes place.
Seine Entscheidung, das Land zu verlassen, war ein Wendepunkt in seinem Leben.
His decision to leave the country was a turning point in his life.
To name the area in which the change takes place, the preposition 'in' is used with the dative. Typical patterns are 'ein Wendepunkt im Leben' (a turning point in life), 'in der Geschichte' (in history), or 'in einer Karriere' (in a career).
Die Schlacht von Stalingrad war ein entscheidender Wendepunkt im Zweiten Weltkrieg.
The Battle of Stalingrad was a decisive turning point in the Second World War.
To emphasize the importance of the turning point, adjectives such as 'entscheidend' (decisive), 'historisch' (historical), 'persönlich' (personal), or 'wichtig' (important) are often used.
Das war ein persönlicher Wendepunkt für mich.
That was a personal turning point for me.
You can immediately recognize the mathematical meaning from words like 'Funktion' (function), 'Graph' (graph), 'Kurve' (curve), or 'Ableitung' (derivative). Outside this context, the general meaning is almost always intended.
Der Lehrer erklärte uns, wie man den Wendepunkt einer Funktion berechnet.
The teacher explained to us how to calculate the inflection point of a function.
crisis
'die Krise' and 'der Wendepunkt' both have to do with an important change in a development. A crisis is a difficult, dangerous situation in which a decision becomes necessary. A turning point is the moment when the direction really changes. The words can be confusing because a crisis often leads to a turning point. 'Krise' describes the problematic situation more. 'Wendepunkt' describes the decisive moment of change more, which can also be positive.
Der neue Job war für Mehmet ein Wendepunkt in seinem Leben.
The new job was a turning point in Mehmet's life.
In der Krise musste die Familie entscheiden, ob sie das Geschäft weiterführt.
During the crisis, the family had to decide whether to keep running the business.