Differential Theorems


Rolle's Theorem
If exists in interval and , then there is a value for which holds true.

Mean-value Theorem
If exists in interval , then there is a value for which holds true.

L'Hospital's Theorem
Let be differentiable near , and and .
If exists, then

Taylor's Theorem
If is differentiable times in an interval including , then there is a value that satisfies


( exists between and ).

Maclaurin's Theorem
If is differentiable times in an interval including 0, then there is a value that satisfies
( exists between 0 and ).

Taylor series/Maclaurin series
When is differentiable an infinite number of times and



Example of Maclaurin series

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