Increasing and Decreasing Function
With the help of the mean value theorem, we can find whether a function is increasing or decreasing.
Increasing Function
The function y = f(x) is said to be an increasing function of x in the interval (a, b),
If the derivative of the f(x) is positive in the interval (a, b) i.e.
f'(x) > 0 for a x ∈ (a, b)
Decreasing Function
The function y = f(x) is said to be a decreasing function of x in the interval (a, b)
If the derivative of the f(x) is negative in the interval (a, b) i.e.
f'(x) < 0 for a x ∈ (a, b)
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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.