Lesson 8 – Some Applications of the Derivative
1
Lesson 8
Some Applications of the Derivative
Equations of Tangent Lines
The first applications of the derivative involve finding the slope of the tangent line and
writing equations of tangent lines.
Example 1:
Find the equation of the line tangent to
2
3
)
(

=
x
x
x
f
at the point
2
1
,
2
.
Example 2:
Find the equation of the line tangent to
)
1
7
ln(
)
(
+
=
x
x
f
when x = 2.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2
Horizontal Tangent Lines, etc.
Some other basic applications involve finding where the slope of the tangent line is equal
to a given number.
Example 3:
Find all values of x for which the slope of the tangent line to
x
x
x
f
ln
2
3
)
(

=
is horizontal.
Example 4:
Suppose
2
3
3
2
)
(
x
x
x
f

=
.
Find all values of x for which
4
)
(
'
=
x
f
.
Note:
In some cases you may need to use the quadratic formula to solve quadratic
equations.
a
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 CONSTANTE
 Equations, Derivative, Slope, 2 seconds, Basic Applications

Click to edit the document details