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

Step 1 ：Step 1: First, remember that the difference quotient is defined as \[\frac{f(x + h) - f(x)}{h}\]

Step 2 ：Step 2: Substitute \(f(x + h)\) and \(f(x)\) into the formula. \[\frac{(3(x + h)^2 + 2(x + h) + 1) - (3x^2 + 2x + 1)}{h}\]

Step 3 ：Step 3: Expand and simplify the numerator.\[\frac{(3x^2 + 6xh + 3h^2 + 2x + 2h + 1) - (3x^2 + 2x + 1)}{h}\] \[=\frac{6xh + 3h^2 + 2h}{h}\]

Step 4 ：Step 4: Cancel out \(h\) from the numerator and denominator. \[= 6x + 3h + 2\]