Mean Value Theorem and Rolle's Theorem

[Jason76]

The 1st goal of the mean value theorem is to find the slope of the secant line. The 2nd goal is to find a point on the function which has the same slope as a secant line. But doesn't the derivative itself have something to do with the secant line?

The main goal of Rolle's theorem is to find a point between two points which has a derivative of 0. Before doing so one must make sure the two points have the same y value.

Any mistakes in this reasoning?

 

[srmichael]

The 1st goal of the mean value theorem is to find the slope of the secant line. The 2nd goal is to find a point on the function which has the same slope as a secant line. But doesn't the derivative itself have something to do with the secant line?

The main goal of Rolle's theorem is to find a point between two points which has a derivative of 0. Before doing so one must make sure the two points have the same y value.

Any mistakes in this reasoning?

MVT: 1) f(x) must be continuous on [a,b]
2) f(x) must be differentiable on (a,b)
3) f(a) not equal to f(b)

RT: 1) f(x) must be continuous on [a,b]
2) f(x) must be differentiable on (a,b)
3) f(a) = f(b)