MAC 2233 Techniques of Differentiation
Section 2.2
h
In section 2.1 we learned that the derivative,
written f’(x), is simply the slope of a tangent line.
h
Using
h
x
f
h
x
f
h
)
(
)
(
lim
0
−
+
→
we can find the slope of any
function at any given xvalue.
h
But what if the function was
25
42
95
99
100
4
3
4
)
(
x
x
x
x
x
x
f
+
+
−
=
?
Finding
h
x
f
h
x
f
h
)
(
)
(
lim
0
−
+
→
would be quite a task!!
h
In this section we will look at shortcuts to finding
the derivative (slope of the tangent line formula)
without having to use
h
x
f
h
x
f
h
)
(
)
(
lim
0
−
+
→
.
Techniques to finding the derivative
1.
If a function
)
(
x
f
is a constant function, i.e.
)
(
x
f
=
# (it is a horizontal line), then the derivative is
zero,
.
0
)
(
'
=
x
f
h
This should make sense since the slope of a
horizontal line is 0 everywhere.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentExamples.
Find f’(x) for the following:
i.
f(x) = 2
f’(x) = 0
ii.
f(x) = 1/2
f’(x) = 0
iii.
f(x) = 0.234
f’(x) = 0
iv.
f(x) =
π
f’(x) = 0
2.
Functions that can be
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '10
 delarosa
 Calculus, Derivative, Slope, right form

Click to edit the document details