Numerical analysis

One of the most important theorems in calculus is the Mean Value Theorem (MVT), which is used to prove many theorems of both differential and integral calculus, as well as other subjects such as numerical analysis. MVT is said to be the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance. The proof of the Mean-Value Theorem is based on a special case of it known as Rolle’s Theorem.

— Numerical analysis

A numerical equation is said to be analysed as soon as we discover the several limits, or pairs of numbers, within which all its unequal real roots lie individually, and its equal roots in distinct groups; that is, as soon as these unequal roots, and groups of equal roots, are all separated and severally enclosed, each between two assignable numbers.

— Numerical analysis