SOLUTION: Determine the difference quotient f(x+h)-f(x)/ h. f(x)=9x^2-2

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Question 841212: Determine the difference quotient f(x+h)-f(x)/ h. f(x)=9x^2-2

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Notation is important. You wrote this:
f%28x%2Bh%29-f%28x%29%2F+h
but you really mean this:
highlight_green%28highlight_green%28%28f%28x%2Bh%29-f%28x%29%29%2F+h%29%29

Just form the expression using f%28x%29=9x%5E2-2 and simplify.
%289%28x%2Bh%29%5E2-2-%289x%5E2-2%29%29%2Fh
%289%28x%5E2%2B2xh%2Bh%5E2%29-2-%289x%5E2-2%29%29%2Fh
%289x%5E2%2B18xh%2B9h%5E2-2-9x%5E2%2B2%29%2Fh----look carefully in numerator for additive inverses
%2818xh%2B9h%5E2%29%2Fh
highlight%2818x%2B9h%29