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.

81. f(x) = x^2 - 4

82. f(x) = 3x^2 + 2

[Eigenvalue]

[tex]\frac{(x+h)²-4-(x²-4)}{h}[/tex]

=[tex]\frac{x²+2hx+h²-x²}{h}[/tex]

=[tex]\frac{2hx+h²}{h}[/tex]

=2x+h

[Eigenvalue]

[tex]\frac{3(x+h)²+2-(3x²+2)}{h}[/tex]

=[tex]\frac{3x²+6xh+3h²-3x²}{h}[/tex]

=[tex]\frac{6xh+3h²}{h}[/tex]

=6x+3h

[nycmath]

[tex]\frac{(x+h)²-4-(x²-4)}{h}[/tex]

=[tex]\frac{x²+2hx+h²-x²}{h}[/tex]

=[tex]\frac{2hx+h²}{h}[/tex]

=2x+h

Very good. By the way, there is one difference quotient of f post that remains unanswered. Would you like to try it out?

[nycmath]

[tex]\frac{3(x+h)²+2-(3x²+2)}{h}[/tex]

=[tex]\frac{3x²+6xh+3h²-3x²}{h}[/tex]

=[tex]\frac{6xh+3h²}{h}[/tex]

=6x+3h

I hope you like my selection of questions. Some will be posted from the David Cohen textbook in just a little while.