SOLUTION: I don't understand this: For f(x) = -3x^2 + 3x + 1, find ( f(4+h) - f(4) ) / h . Simplify completely. Any help would be greatly appreciated! Thanks!

Algebra ->  Functions -> SOLUTION: I don't understand this: For f(x) = -3x^2 + 3x + 1, find ( f(4+h) - f(4) ) / h . Simplify completely. Any help would be greatly appreciated! Thanks!      Log On


   

Question 905095: I don't understand this:
For f(x) = -3x^2 + 3x + 1, find ( f(4+h) - f(4) ) / h . Simplify completely.
Any help would be greatly appreciated! Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+-3x%5E2+%2B+3x+%2B+1
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First we need to find f(x+h)

f%28x%29+=+-3x%5E2+%2B+3x+%2B+1

f%28x%2Bh%29+=+-3%28x%2Bh%29%5E2+%2B+3%28x%2Bh%29+%2B+1 Replace every x with x+h. Then expand.

f%28x%2Bh%29+=+-3%28x%5E2%2B2xh%2Bh%5E2%29+%2B+3%28x%2Bh%29+%2B+1

f%28x%2Bh%29+=+-3x%5E2-6xh-3h%5E2+%2B+3x%2B3h+%2B+1

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Now we plug in f%28x%2Bh%29+=+-3x%5E2-6xh-3h%5E2+%2B+3x%2B3h+%2B+1 and f%28x%29+=+-3x%5E2+%2B+3x+%2B+1 into %28f%28x%2Bh%29-f%28h%29%29%2Fh

Simplify as much as possible





%28f%28x%2Bh%29-f%28h%29%29%2Fh+=+%28-6xh-3h%5E2%2B3h%29%2Fh

%28f%28x%2Bh%29-f%28h%29%29%2Fh+=+%28h%28-6x-3h%2B3%29%29%2Fh



%28f%28x%2Bh%29-f%28h%29%29%2Fh+=+%28cross%28h%29%28-6x-3h%2B3%29%29%2F%28cross%28h%29%29

%28f%28x%2Bh%29-f%28h%29%29%2Fh+=+-6x-3h%2B3

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Finally, we plug in x = 4

%28f%28x%2Bh%29-f%28h%29%29%2Fh+=+-6x-3h%2B3

%28f%284%2Bh%29-f%28h%29%29%2Fh+=+-6%284%29-3h%2B3

%28f%284%2Bh%29-f%28h%29%29%2Fh+=+-24-3h%2B3

%28f%284%2Bh%29-f%28h%29%29%2Fh+=+-21-3h

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The final answer is %28f%284%2Bh%29-f%28h%29%29%2Fh+=+-21-3h