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## Main Question or Discussion Point

I'd like the geometric meaning of the Mean Value Theorem. Say for instance I had a function of velocity that varied as [tex]t^{3}[/tex] + [tex]3t^{2}[/tex] + 3t +1. I consider the interval [0,4].

So by MVT, I have a number c in [0,4] such that f'(c)(4) = f(4) - f(0). What does that mean? That there is an accelaration in that interval equal to the net change in accelaration? Meaning that the slope at 4 minus the slope at 0 is equal to the net change in slope?

Could someone PLEASE explain?

So by MVT, I have a number c in [0,4] such that f'(c)(4) = f(4) - f(0). What does that mean? That there is an accelaration in that interval equal to the net change in accelaration? Meaning that the slope at 4 minus the slope at 0 is equal to the net change in slope?

Could someone PLEASE explain?