low point
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low point
The worst moment or the worst phase in a development, a relationship, or a person's life.
Die Niederlage im Finale war der absolute Tiefpunkt der Saison für die Mannschaft.
The defeat in the final was the absolute low point of the season for the team.
lowest point
The physically or geographically lowest point of an object, a curve, or an area of land.
Am Tiefpunkt der Schlucht fließt ein kleiner Bach.
A small stream flows at the lowest point of the gorge.
'Tiefpunkt' (low point) is a compound noun made from the adjective 'tief' (deep/low) and the noun 'der Punkt' (point). So it literally describes the lowest or deepest point of something.
Nach diesem Streit erreichte ihre Freundschaft einen Tiefpunkt.
After this argument, their friendship reached a low point.
In its figurative meaning, 'Tiefpunkt' (low point) is often used with verbs such as 'erreichen' (to reach), 'überwinden' (to overcome), or 'darstellen' (to represent/constitute). A common intensifier is 'der absolute Tiefpunkt' (the absolute low point).
Die Mannschaft hat den Tiefpunkt der Saison nun hoffentlich überwunden.
The team has now hopefully overcome the low point of the season.
You can recognize the physical meaning from geographical or scientific terms such as 'Tal' (valley), 'Kurve' (curve), or 'Temperatur' (temperature). Abstract terms such as 'Karriere' (career), 'Stimmung' (mood), or 'Beziehung' (relationship) point to the figurative meaning.
Die Temperatur erreichte heute Nacht ihren Tiefpunkt.
The temperature reached its lowest point tonight.
minimum
For a function, the Minimum is the smallest value it takes. The Tiefpunkt, by contrast, is the corresponding point on the graph and includes both this value and its position. Minimum is therefore the appropriate term for the value, while Tiefpunkt is the appropriate term for the point.
Der Tiefpunkt des Graphen liegt bei (3|2).
The lowest point of the graph is at (3, 2).
Das Minimum der Funktion ist 2.
The minimum of the function is 2.
