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Question 198110: use the definition of derivative to f'(x) when f(x)=x^2-5x+1
not getting it
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! use the definition of derivative to f'(x) when f(x)=x^2-5x+1
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You need to find "the limit of [f(x+h)-f(x)]/h as h goes to zero"
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f(x+h) = (x+h)^2 - 5(x+h) + 1
= x^2 + 2hx + h^2 - 5x -5h +1
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f(x) = x^2 -5x +1
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So f(x+h) - f(x) = 2hx + h^2 -5h
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Then, dividing by h, you get [f(x+h)-f(x)]/h = 2x + h -5
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Now take the limit as h goes to zero and you get:
f'(x) = 2x - 5
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Hope that helps.
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Cheers,
Stan H.
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