Precalculus Question? Difference Quotient For The Function
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Precalculus Question? Difference Quotient For The Function

[From: ] [author: ] [Date: 12-07-02] [Hit: ]
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Calculate and simplify the difference quotient for the function

y=x^3-125

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[ f(x+h) – f(x)] / h =
[ (x+h)³ – 125 – (x³ – 125)] / h =
[ x³ + 3x²h + 3xh² + h³ – 125 – x³ + 125] / h =
[ 3x²h + 3xh² + h³ ] / h =
3x² + 3xh + h²
and in the limit, as h → 0, that's just 3x²
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