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2]Mean Value Theorem & Rolle’s Theorem | Calculus | Engineering Mathematics
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In last tutorial we covered the basics required for Mean Value Theorem. In this video tutorial, we will first understand the Mean Value Theorem, then switch to special case of mean value theorem called “Rolle’s theorem” and understand the through one example.
Statement or definition of Mean Value Theorem:
If function is continuous on closed interval [a,b] and differentiable on open interval (a,b), then there exist a point c in the open interval (a,b) such that f’(c) = f(b) - f(a) / b-a
This simply, means that slope at point c is equal to the slope that joins points a and b. Secant joining endpoints [a,b] is parallel to the tangent at c.
Mean Value Theorem is explained through graphical representation.
Rolle’s Theorem:
Let function be continuous on closed interval [a,b] and differentiable on open interval (a,b). If f(a) is equal to f(b), then there is atleast one point c in (a,b) for which f’(c) = 0. If either condition continuity or differentiability fails, Rolle’s Theorem fails.
This statement is explained through one example.
Consider function f(x) = (x - 4) raise to 2 +1 from [2,5]
Check out the video tutorial for more better explanation.
Link to view all playlists:
Statement or definition of Mean Value Theorem:
If function is continuous on closed interval [a,b] and differentiable on open interval (a,b), then there exist a point c in the open interval (a,b) such that f’(c) = f(b) - f(a) / b-a
This simply, means that slope at point c is equal to the slope that joins points a and b. Secant joining endpoints [a,b] is parallel to the tangent at c.
Mean Value Theorem is explained through graphical representation.
Rolle’s Theorem:
Let function be continuous on closed interval [a,b] and differentiable on open interval (a,b). If f(a) is equal to f(b), then there is atleast one point c in (a,b) for which f’(c) = 0. If either condition continuity or differentiability fails, Rolle’s Theorem fails.
This statement is explained through one example.
Consider function f(x) = (x - 4) raise to 2 +1 from [2,5]
Check out the video tutorial for more better explanation.
Link to view all playlists:
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