One by one we will discuss each theorem with the help of video tutorials. Rolle’s Theorem, Lagrange’s Mean Value Theorem, and Cauchy’s Mean Value Theorems are related to each other. Watch each video attentively to understand each theorem completely.
1. Rolle’s Theorem
If a function is continuous in the closed interval a to b, it is differentiable in the open interval a to b, and function values are same at the
2. Lagrange’s Mean Value Theorem
Lagrange’s Mean Value Theorem is derived from Rolle’s Theorem. If a function is continuous in a given closed interval, and it is differentiable in the given open interval. Then there is at least one value of c, between the given interval, the tangent at which is parallel to the line joining endpoints of the interval. Watch the video lecture to grab this concept.
3. Cauchy’s Mean Value Theorem
Cauchy’s Mean Value Theorem is the extension of the Lagrange’s Mean Value Theorem. If two functions are continuous in the given closed interval, are differentiable in the given open interval, and the derivative of the second function is not equal to zero in the given interval. Then there is at least one value of c between the given interval such that the ratio of the difference of the function values at the endpoints of the first function to the second function is same as the ratio of the slope at c of first to the second function. See the video tutorial to learn it visually.
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