Math Video | Calculus Lesson | Differential Calculus 431

Author

centerofmath

Title

4: Extrema and the Mean Value Theorem

Video Description

The derivative is defined in such a way that it is the instantaneous rate of change. Intuitively, then, there are a number of things which we expect to be true. We expect that if the derivative is positive, the function increases as the variable increases, and if the derivative is negative, the function decreases as the variable increases. For instance, if the rate of change, with respect to time, of the money that you have is positive, you should have more money as time increases…Finally and most obviously, shouldn’t it be true that, if the rate of change of a quantity is zero, then that quantity is constant? Note that what we already know is that the derivative of a constant function is zero. However, we don’t have any theorem (yet) telling us that, if the derivative is zero, then the function had to be constant.

Video Keywords

Differential Calculus, Center of Math, David B. Massey, Calc 1, Extrema, Mean Value Theorem, Single-Variable Calculus

Category