Expert: Paul Klarreich - 5/25/2007

Question
LET F(X)=4XSQUARED-9

COMPUTE: F(X)=F(X+h)-F(X)/h

Answer
Questioner:   ABBY
Category:  Advanced Math
 
Subject:  PRE-CAL HELP
Question:  LET F(X)=4XSQUARED-9

COMPUTE: F(X)=F(X+h)-F(X)/h
................................................
Hi, Abby,

Request:  In the future, keep your fingers off that Caps Lock key.  Using capitals in messages is the equivalent of shouting and is considered bad manners.

Now, then, for your example.  In doing these examples (it's called the Difference Quotient) the trick is to make good and careful use of parentheses.

f(x) = 4x^2 - 9

f(x + h) = 4(x + h)^2 - 9
        = 4(x^2 + 2xh + h^2) - 9
        = 4x^2 + 8xh + 4h^2 - 9

f(x + h) - f(x) = 4x^2 + 8xh + 4h^2 - 9 - (4x^2 - 9)
= 4x^2 + 8xh + 4h^2 - 9 - 4x^2 + 9
=        8xh + 4h^2

f(x + h) - f(x)    8xh + 4h^2
--------------- = ------------
     h                h

 (8x + 4h)h
= ---------- = 8x + 4h
     h

That's it.  A clue for the future:  That h on the bottom is bad news.  You must find a way to cancel it, but make sure you don't commit any algebraic 'crimes'.