[1.7]
Coaxing the Derivative out of NOTHING!
First we start with
( )
y
f x
and what we know about AROC at
x
a
slope of the secant from (
,
(
)) to (
,
(
))=
(
)
( )
AROC of
x
a
a f a
a
h f a
h
f a
h
f a
y
f
h
x
Now
As
h
gets smaller and smaller and smaller the length of the secant line gets ever
smaller, but at the same time the slope of the secant line gets ever closer to the slope of the
tangent line.
E
ven though we don’t really know the value of the slope of the tange
nt line we
know the secant line slope is getting closer to it.
For small
the slope of the secant from
(
)
( )
Slope of the tangent to
at the input x
h
f a
h
f a
f
h
Now for zee Magic…Vee do zee CALCULUS
und
The secant line disappears, thus ceases to exist and therefore has no slope at the same
“moment” that it
s slope becomes the slope of the tangent line.
We say the AROC is no longer
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 asd
 Calculus, Derivative, Slope, ZEE

Click to edit the document details