THE DIFFERENCE QUOTIENT
I.
The ability to set up and simplify difference quotients is essential for calculus students.
It is
from the difference quotient that the elementary formulas for derivatives are developed.
II.
Setting up a difference quotient for a given function requires an understanding of function
notation.
III.
Given the function:
f(x) =
2
3x
4
x5
−−
A.
This notation is read “f of x equals . . .”.
B.
The implication is that the value of the function (the yvalue) depends upon the
replacement for “x”.
C.
If a number is substituted for “x”, a numerical value for the function is found.
D.
If a nonnumerical quantity is substituted for “x”, an expression is found rather than
a numerical value.
E.
Careful use of parentheses is essential!
IV.
Examples using f(x) =
2
4
A.
2
f(4)
3(4)
4(4
)5
27
=
−
−
=
B.
2
f( 3)
3( 3)
4( 3
34
−
=
−
−−−
=
C.
f(a) =
2
3a
4
a5
D.
2
f(2a
3)
3(2a
3)
4(2a
3
−
=
−
−
2
3(4a
12a
9)
8a
1
25
=
−
+
−
+
−
=
22
12a
36a
27
8a
1
12a
44a
34
−
+
−
+
−
=
−
+
E.
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.
 Fall '14
 Fraction, Elementary arithmetic, Rational function, Mathematics in medieval Islam, 4H

Click to edit the document details