SOLUTION: If {{{ f(x)=3x^2-4x-5 }}}, find {{{ (f(x+h)-f(x))/h }}}.

Algebra ->  Functions -> SOLUTION: If {{{ f(x)=3x^2-4x-5 }}}, find {{{ (f(x+h)-f(x))/h }}}.      Log On


   

Question 1064909: If +f%28x%29=3x%5E2-4x-5+, find +%28f%28x%2Bh%29-f%28x%29%29%2Fh+.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Question: If +f%28x%29=3x%5E2-4x-5+, find +%28f%28x%2Bh%29-f%28x%29%29%2Fh+.


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Steps:


First we need to find f%28x%2Bh%29


f%28x%29=3x%5E2-4x-5


f%28x%2Bh%29=3%28x%2Bh%29%5E2-4%28x%2Bh%29-5 Replace every copy of x with x+h


f%28x%2Bh%29=3%28x%5E2%2B2xh%2Bh%5E2%29-4%28x%2Bh%29-5 Expand out (x+h)^2


f%28x%2Bh%29=3x%5E2%2B6xh%2B3h%5E2-4x-4h-5 Distribute


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Now we can compute +%28f%28x%2Bh%29-f%28x%29%29%2Fh+








%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%286xh%2B3h%5E2-4h%29%2F%28h%29


%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28h%286x%2B3h-4%29%29%2F%28h%29





%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28cross%28h%29%286x%2B3h-4%29%29%2F%28cross%28h%29%29


%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+6x%2B3h-4


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Final Answer: 6x%2B3h-4