Mean Value Theorem
Chapter Name : Continuity And Differentiability |
Sub Topic Code : 104_12_05_08_01 |
Topic Name : Mean Value Theorem |
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Sub Topic Name : Mean Value Theorem |
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Introduction
Mean Value Theorem and its implementation.
Pre-Requisites:
Finding derivative using chain rule , Knowledge of functions.
Activity:
Implementation and Verification of MVT or Rolle’s Theorem.
Real Life Question:
Where the derivative of function is zero.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Mean Value or Rolle’s theorem | Let f : [a, b] R be continuous on [a, b] and differentiable on (a, b), such that f(a) = f(b), where a and b are some real numbers. Then there exists some c in (a, b) such that f’(c) = 0. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Take any differentiable function | Verify the Rolle’s Theorem for the function and find the point ‘c’ where f’(c) = 0. |
Real life uses :
Finding the maximum and minimum point.
Practical examples around us
| Examples | Explainations |
|---|---|
| y=x^2+5 | Verify Rolle’s Theorem if a = -4, b = 4. |
What you learn in Theory:
Verifying Mean Value or Rolle’s Theorem.
What you learn in Practice:
Finding the point in the domain where slope is zero.