Serlo: EN: Constant functions

{{#invoke:Mathe für Nicht-Freaks/Seite|oben}}

"A function is constant, if its derivative vanishes", i.e. $f^{\prime }(x)=0$. This is the main statement which we want to make concrete in this article.

Identity theorem of differential calculus Vorlage:Anker

The first conclusion of $f^{\prime }=0$ implying that a function is constant is that functions with identical derivatives are identical except for one constant. This result will prove very useful later on in the fundamental theorem of calculus.

Exercises

Interval assumption for constant functions

The condition that the function $f$ is defined on an interval is necessary for the criterion for constancy! This is illustrated by the following task:

Trigonometric Pythagorean theorem

Using the criterion for constancy, identities of functions can also be proven very well:

Characterization of sin and cos

{{#invoke:Mathe für Nicht-Freaks/Seite|unten}}