# L10 - Lecture 10 The Derivative Function In the last...

This preview shows pages 1–4. Sign up to view the full content.

Lecture 10 — The Derivative Function In the last examples of Lecture 9, we saw that, from a function f , we could derive a new function that represents the slope (or instantaneous rate of change) of f at each x = a . This function is called the derivative of f , and we give it the special nota- tion f 0 . Thus, f 0 ( a ) = or equivalently, if we let h = x - a , f 0 ( a ) = Other notations Interpretations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The process of ﬁnding the derivative of a function is called differentiation . Note the derivative is deﬁned as a limit, which may or may not exist. If f 0 ( a ) exists, we say that f is differentiable at a . We say it is differentiable on an interval I if it is differentiable at each point in I . On what interval(s) is the function V ( t ) = ( t 2 + t ) 1 3 differentiable?
f is differentiable at a , then it is continuous at a . Beyond calculus: The world is full of wild functions that are continuous, but nowhere differentiable, like the stock market. They have NO derivative and cannot be drawn—calculus cannot handle them. Some causes for functions to be not differentiable:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

L10 - Lecture 10 The Derivative Function In the last...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online