Mean Value Theorem
State Mean value theorem.
For any function f(x) such that f(x) is continuous in [a, b] and f(x) is differentiable in (a, b) then according to Mean Value Theorem,
There exist a c in the interval [a, b] such that,
f'(c) = [f(b)–f(a)]/(b-a)
What is Rolle’s Theorem?
Rolle’s Theorem states that for any function f(x) such that f(x) is continuous in [a, b] and f(x) is differentiable in (a, b) then there exists a point c in the [a, b] such that the tangent at point is parallel to the x-axis.
What is the Mean Value Theorem Equation?
The mean value theorem equation is,
f'(c) = [ f(b) – f(a) ] / (b – a)
which is applicable on f(x): [a, b]→ R such that f(x) is continuous in [a, b] and f(x) is differentiable in (a, b)
What is the Difference Between Mean Value Theorem and Intermediate Value Theorem?
For any continuous function, f(x) is continuous on [a, b] and differentiable on (a, b),
- According to the Mean Value Theorem, there exists a ‘c’ in the interval (a, b) such that f'(c) = [ f(b) – f(a) ] / (b – a).
- According to the Intermediate Value Theorem, for any L between f(a) and f(b), there exists a ‘c’ in the interval (a, b) such that f(c) = L.
What is Mean Value Theorem Formula?
The mean value theorem formula is,
f’(c) = [f(b) – f(a)]/(b-a)
Mean Value Theorem
Mean Value Theorem is one of the important theorems in calculus. Mean Value Theorem states that for a curve passing through two given points there exist at least one point on the curve where the tangent is parallel to the secant passing through the two given points. Mean Value Theorem is abbreviated as MVT. This theorem was first proposed by an Indian Mathematician Parmeshwara early 14th century. After this various mathematicians from all around the world worked on this theorem and the final theorem was proposed by Augustin Louis Cauchy in the year 1823.
Let’s learn about Mean Value Theorem its Geometrical Interpretation and others in detail in this article.