HELP with this Math Problem Please!
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HELP with this Math Problem Please!

[From: ] [author: ] [Date: 12-09-11] [Hit: ]
......
Hi guys, I don't know how to do this problem:

Find and simplify
[f(x + h) − f(x)] / h where (h ≠ 0)

for the function.
f(x) = 6x^2 − 4x + 7

-
f(x+h) = 6(x+h)² − 4(x+h) + 7
  = 6(x² + 2xh + h²) − 4x − 4h + 7
  = 6x² + 12xh + 6h² − 4x − 4h + 7

f(x+h) − f(x) = 6x² + 12xh + 6h² − 4x − 4h + 7 − (6x² − 4x + 7)
  = 12xh + 6h² − 4h
  = h(12x + 6h − 4)

[f(x+h) − f(x)] / h = h(12x + 6h − 4) / h

For h ≠ 0 we may cancel the common factor of h in the numerator and denominator, leaving us with

[f(x+h) − f(x)] / h = 12x + 6h − 4
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