SOLUTION: I need some help please f(x)=3x^2-5x+2, find [f(x+h)-f(x)}/h] please help Thank you

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Question 58211: I need some help please
f(x)=3x^2-5x+2, find [f(x+h)-f(x)}/h]
please help
Thank you
Found 2 solutions by stanbon, hayek:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=3x^2-5x+2, find [f(x+h)-f(x)}/h
f(x+h)= 3(x+h)^2-5(x+h)+2
=3x^2+6hx+3h^2-5x-5h+2
=(3x^2-5x+2) +6hx+3h^2-5h
Then f(x+h)-f(x) = 6hx+3h^2-5h
And finally [f(x+h)-f(x)]/h = [6hx+3h^2-5h)/h
=6x+3h-5
Cheers,
Stan H.

Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
First, find f(x+h):
f%28x%2Bh%29=3%28x%2Bh%29%5E2-5%28x%2Bh%29%2B2
f%28x%2Bh%29=3%28x%5E2%2B2xh%2Bh%5E2%29-5x-5h%2B2
f%28x%2Bh%29=3x%5E2%2B6hx%2B3h%5E2-5x-5h%2B2
f%28x%2Bh%29=highlight%283x%5E2%2B%286h-5%29x%2B%283h%5E2-5h%2B2%29%29
Now write the problem:
%28f%28x%2Bh%29-f%28x%29%29%2Fh=%28highlight%283x%5E2%2B%286h-5%29x%2B%283h%5E2-5h%2B2%29%29-%283x%5E2-5x%2B2%29%29%2Fh
=%28cross%283x%5E2%29%2B%286h-5%29x%2B%283h%5E2-5h%2B2%29-cross%283x%5E2%29%2B5x-2%29%2Fh
=%28%286h-5%2B5%29x%2B%283h%5E2-5h%2B2-2%29%29%2Fh
=%286hx%2B3h%5E2-5h%29%2Fh
highlight%28%28f%28x%2Bh%29-f%28x%29%29%2Fh=6x-5%2B3h%29
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Note that when you take the limit as h nears 0, you have the formula for the slope of the curve at each point (x) along the curve.