We normally use the word abrupt.
- Abruptness, for a descriptive noun.
- Abrupt change.
- Acute change.
Frequently, people use sudden and abrupt interchangeably. However, there is a significant difference between sudden and abrupt.
Sudden should be restricted to abruptness in the time dimension. Whereas, abrupt is applicable to any "sudden" change in any dimension.
However, it is risky to use acute when trying to describe a mathematical chart or phenomenon in lay terms, because there is confusion between its meanings mathematically (in geometry) and colloquially.
"Please be careful, there is an abrupt change in the speed limit from 70 mph to 35 mph at that stretch of the road. After which, there will be an abrupt bend." The instructor said suddenly.
We were surprised when we noticed the abrupt change in the curve. The rate of increase in pressure abruptly decreased with the increase in temperature.
From American Heritage Dictionary ...
1. Unexpectedly sudden: an abrupt change in the weather.
2. Surprisingly curt; brusque: an abrupt answer made in anger.
3. Touching on one subject after another with sudden transitions: abrupt prose.
4. Steeply inclined. See Synonyms at steep1.
5. Botany Terminating suddenly rather than gradually; truncate: an abrupt leaf.
Compare with ...
1. Happening without warning; unforeseen: a sudden storm.
2. Characterized by hastiness; abrupt or rash: a sudden decision. See Synonyms at impetuous.
3. Characterized by rapidity; quick and swift.
all of a sudden
Very quickly and unexpectedly; suddenly.
1. Having a sharp point or tip.
2. Keenly perceptive or discerning: "a raw, chilling and psychologically acute novel of human passions reduced to their deadliest essence" (Literary Guild Magazine). See Synonyms at sharp.
3. Reacting readily to stimuli or impressions; sensitive: His hearing was unusually acute.
4. Of great importance or consequence; crucial: an acute lack of research funds.
5. Extremely sharp or severe; intense: acute pain; acute relief.
a. Having a rapid onset and following a short but severe course: acute disease.
b. Afflicted by a disease exhibiting a rapid onset followed by a short, severe course: acute patients.
7. Music High in pitch; shrill.
8. Geometry Having an acute angle: an acute triangle.