SOLUTION: Compute and simplify the difference quotient (f(x+h)-f(x))/h, h=/0 f(x)= 3x^2 +5x

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Question 1126442: Compute and simplify the difference quotient (f(x+h)-f(x))/h, h=/0
f(x)= 3x^2 +5x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+3x%5E2+%2B5x Given function

f%28x%29=+3%28x%29%5E2+%2B5%28x%29 Place parenthesis around each x. The parenthesis will help with FOIL and distributive steps later on.

f%28x%2Bh%29=+3%28x%2Bh%29%5E2+%2B5%28x%2Bh%29 Replace every x with x+h

f%28x%2Bh%29=+3%28x%5E2%2B2xh%2Bh%5E2%29+%2B5%28x%2Bh%29 FOIL

f%28x%2Bh%29=+3x%5E2%2B6xh%2B3h%5E2+%2B5x%2B5h Distribute

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Stuff in red is f(x+h); stuff in green is f(x)



Distribute

%28f%28x%2Bh%29-f%28x%29%29%2F%28h%29+=+%286xh%2B3h%5E2%2B5h%29%2F%28h%29 Combine like terms

%28f%28x%2Bh%29-f%28x%29%29%2F%28h%29+=+%28h%286x%2B3h%2B5%29%29%2F%28h%29 Factor out h

Divide and cancel

%28f%28x%2Bh%29-f%28x%29%29%2F%28h%29+=+6x%2B3h%2B5 Final Answer