Difference Quotient

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.1

Find the difference quotient of f; that is find
[f(x + h) - f(x)]/h, h cannot be 0, for each function. Be sure to simplify.

79. f(x) = 4x + 3

80. f(x) = -3x + 1

[Eigenvalue]

[tex]\frac{4x+4h+3-4x-3}{h}[/tex]

=[tex]\frac{4h}{h}[/tex]

=4

[tex]\frac{-3x-3h+1+3x-1}{h}[/tex]

=[tex]\frac{-3h}{h}[/tex]

=-3

[Eigenvalue]

Generalized difference quotient for ax+b
[tex]\frac{a(x+h)+b-(ax+b)}{h}[/tex]

=[tex]\frac{ax+ah-ax}{h}[/tex]

=[tex]\frac{ah}{h}[/tex]
=a

[nycmath]

[tex]\frac{4x+4h+3-4x-3}{h}[/tex]

=[tex]\frac{4h}{h}[/tex]

=4

[tex]\frac{-3x-3h+1+3x-1}{h}[/tex]

=[tex]\frac{-3h}{h}[/tex]

=-3

Fun times woth the difference quotient of f problems.

[nycmath]

Generalized difference quotient for ax+b
[tex]\frac{a(x+h)+b-(ax+b)}{h}[/tex]

=[tex]\frac{ax+ah-ax}{h}[/tex]

=[tex]\frac{ah}{h}[/tex]
=a

Smooth sailing through the textbook.