Existence Theorems

Definition

Existence Theorems are mathematical statements that guarantee the existence of solutions or objects within certain conditions. In calculus, these theorems are often used to prove the existence of critical points, extrema, or solutions to differential equations.

Related terms

Critical Points:

These are points on a graph where either the derivative is zero or does not exist. They play an important role in determining the behavior of a function.

Extrema:

Refers to the maximum and minimum values of a function. Existence Theorems can help prove that these extrema exist within certain intervals.

Differential Equations:

These are equations that involve derivatives and describe how a function changes over time. Existence Theorems can be used to guarantee the existence of solutions to these equations.