Mean Value Theorem: Find the Mean Slope and c Values Such That f'(c) = Mean Slope (Cubic)

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This video explains how to apply the Mean Value Thereom to a cubic function.
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Well explained! The graph really helps illustrate that you are simply finding spots in the open interval where the slope of the tangent line equals the slope of the line that connects the ends of the interval. Is there another video that states the conditions under which there WILL be at least one point where this is true? Refresh my memory: does the function have to be continuous on the CLOSED interval AND differentiable on the OPEN interval?

christinekincaiddewey