🔶34 - Rolle's and Mean Value Theorem Problems 1

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🔶34 - Rolle's and Mean Value Theorem Problems 1

In this video, we shall learn how to show whether of not a given function satisfy Rolle's and Mean Value Theorems, and how to find the value(s) of within the open interval (a,b). This lesson has been divided into two videos.

Rolle's Theorem states that;
Given that f is a function,
1. If f is continuous in [a, b]
2. and f is differentiable in (a,b)
3. and if f(a) = f(b), then there exist at least one c in (a,b)
such that f'(c) = 0.

Mean Value Theorem states that;
Given that f is a function,
1. If f is continuous in [a, b]
2. and f is differentiable in (a,b)
then there exist at least one c in (a,b)
such that f'(c) = f(b) - f(a) / b-a

00:00 - Rolle's Theorem
02:22 - Example 1 - Rolle's Theorem
07:34 - Example 2 - Rolle's Theorem

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Please so if the function is not a polynomial function, how do we directly determine if it's continuous and differentiable at a given point 😢

ebenezerelorm

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