The Mean Value Theorem "MVT".

0:00 The Mean Value Theorem.

0:35 Rolle’s Theorem.

3:23 The Mean Value Theorem "MVT".

5:23 Consequences of the Mean Value Theorem.

5:28 Zero Derivative Implies Constant Function.

9:09 Functions with equal derivatives differ by a constant.

11:36 Example: f(x) = 2 SQRT(x).

14:01 Example: f(x) = x (x-1)^2 over [0,1].

16:36 Example: f(x) = 1-ABS (x) over [-1, 1].

17:23 Example: f(x) = Cos (4x) over [ pi/8, 3pi/ 8].

18:47 Example: f (x) = 1-x^(2/3) over [-1, 1].

19:23 Example: f(x) = x^3-x^2-5x-3 over [-1,3].

20:53 Example: f(x) = 7-x^2 over [-1, 2].

23:45 Example: f(x) = -2x for x less than or equal to 0, and x for x greater than or equal to 0.

25:21 Example: f(x) = ln (2x) over [1, e].