Simplify the difference quotient ƒ(x+h)-ƒ(x)/h
ƒ(x) = 2x² -3x +1

Verified step by step guidance

1. Step 1: Start by substituting the function \( f(x) = 2x^2 - 3x + 1 \) into the difference quotient \( \frac{f(x+h) - f(x)}{h} \).
2. Step 2: Calculate \( f(x+h) \) by replacing \( x \) with \( x+h \) in the function: \( f(x+h) = 2(x+h)^2 - 3(x+h) + 1 \).
3. Step 3: Expand \( f(x+h) \): \( 2(x+h)^2 = 2(x^2 + 2xh + h^2) = 2x^2 + 4xh + 2h^2 \) and \( -3(x+h) = -3x - 3h \). Combine these to get \( f(x+h) = 2x^2 + 4xh + 2h^2 - 3x - 3h + 1 \).
4. Step 4: Substitute \( f(x+h) \) and \( f(x) \) into the difference quotient: \( \frac{(2x^2 + 4xh + 2h^2 - 3x - 3h + 1) - (2x^2 - 3x + 1)}{h} \).
5. Step 5: Simplify the expression by canceling out like terms and dividing each term by \( h \). This will give you the simplified form of the difference quotient.