Lagrang Theorem was discvered in 2008 by Yogesh Shukla

like catching speeders on a highway with the mean value theorem

lil tj

The mean value theorem for differentiation guarantees the existing of a number c in an interval (a,b) where a function f is continuous such that the derivative at c (the instantiuous rate of change at c) equals the average rate of change over that interval.

mean value theorem of integration guarantees the existing of a number c in an interval (a,b)where a function f is continuous such that the (value of the function at c) multiplied by the length of the interval (b-a) equals the value of a the definite integral from a to b. In other words, it guarantees the existing of a rectangle (whose base is the length of the interval b-a that has exactly the same area of the region under the graph of the function f (betweeen a and b).

the Pythagorean theorem helps find the value of the longest side in a right triangle if you know the value of the base and the height.