SOLUTION: For the function f(x) = x² - 3x + 4 construct and simplify the difference quotient f(x) = [f(x+h) – f(x)]/h

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Question 87509: For the function f(x) = x² - 3x + 4 construct and simplify the difference quotient f(x) = [f(x+h) – f(x)]/h

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2+-+3x+%2B+4

f%28x%2Bh%29+=+%28x%2Bh%29%5E2+-3%28x%2Bh%29+%2B4
f%28x%2Bh%29+=+x%5E2+%2B2xh%2B+h%5E2+-3x-3h+%2B4

+%28f%28x%2Bh%29+-f%28x%29%29%2Fh=+%28%28x%5E2%2B2xh%2Bh%5E2+-3x-3h%2B4%29+-%28x%5E2+-3x%2B4%29%29%2Fh+

Remove parentheses
+%28f%28x%2Bh%29+-f%28x%29%29%2Fh=+%28x%5E2%2B2xh%2Bh%5E2+-3x-3h%2B4+-x%5E2+%2B3x-4%29%2Fh+

Combine like terms:
+%28f%28x%2Bh%29+-f%28x%29%29%2Fh=+%282xh%2Bh%5E2+-3h+%29%2Fh+

Factor out the common factor of h:
+%28f%28x%2Bh%29+-f%28x%29%29%2Fh=+%28h%282x%2Bh+-3%29+%29%2Fh+

Divide out the h factor:
+%28f%28x%2Bh%29+-f%28x%29%29%2Fh=+2x%2Bh+-3+

R^2 at SCC