Mean Value Theorem Formula Explanation

Mean Value Theorem Formula Explanation

Maths Formulas

Mean Value Theorem Formula Explanation

 

Mean Value Theorem Formula Explanation (MVT), also known as Lagrange’s mean value theorem (LMVT), and provides a formal framework for a fairly intuitive statement relating the change in a function to the behavior of its derivative. The theorem states that the derivative of a continuous and differentiable function must attain the function’s average rate of change (in a given interval). For instance, if a car travels 100 miles in 2 hours, but then it must have had the exact speed of 50 mph at some point in time.

Mean Value Theorem Formula Explanation

Mean Value Theorem Formula

Suppose that a function f is

  1. continuous on the closed interval [a,b], and
  2. differentiable on the open interval (a,b).

Then, there is a number c such that a<c<b and f'(c)=\frac{f(b)-f(a)}{b-a}.

Simple-sounding as it is, the mean value theorem actually lies at the heart of the proof of the fundamental theorem of calculus and is itself based ultimately on properties of the real numbers. so there is a slight generalization known as Cauchy’s mean value theorem; for a generalization to higher derivatives, see Taylor’s theorem and

 

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