Problem

Find the difference quotient for the function f(x)=3x2−2x+1.

Answer

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Answer

Then, we substitute f(x+h) and f(x) into the formula, giving 3x2+6hx+3h2−2x−2h+1−(3x2−2x+1)h=6hx+3h2−2hh=6x+3h−2.

Steps

Step 1 ：The difference quotient formula is f(x+h)−f(x)h.

Step 2 ：First, we compute f(x+h)=3(x+h)2−2(x+h)+1=3x2+6hx+3h2−2x−2h+1.

Step 3 ：Then, we substitute f(x+h) and f(x) into the formula, giving 3x2+6hx+3h2−2x−2h+1−(3x2−2x+1)h=6hx+3h2−2hh=6x+3h−2.

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