Find the difference quotient for the function \(f(x) = 3x^2 - 2x + 1\).

Step 1 ：Step 1: Recall the formula for the difference quotient: \(\frac{f(x+h) - f(x)}{h}\)

Step 2 ：Step 2: Substitute \(f(x) = 3x^2 - 2x + 1\) into the equation to get \(\frac{f(x+h) - f(x)}{h} = \frac{3(x+h)^2 - 2(x+h) + 1 - (3x^2 - 2x + 1)}{h}\)

Step 3 ：Step 3: Simplify to get \(\frac{3(x^2 + 2xh + h^2) - 2x - 2h + 1 - 3x^2 + 2x - 1}{h}\)

Step 4 ：Step 4: Combine like terms and simplify further to get \(\frac{6xh + 3h^2 - 2h}{h}\)

Step 5 ：Step 5: Cancel out h in the numerator and the denominator to get \(6x + 3h - 2\)

Step 6 ：Step 6: Take the limit as h approaches 0 to find the difference quotient: \(6x + 3(0) - 2 = 6x - 2\)