Problem

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

Answer

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Answer

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

Steps

Step 1 ：Step 1: Recall the formula for the difference quotient: f(x+h)−f(x)h

Step 2 ：Step 2: Substitute f(x)=3x2−2x+1 into the equation to get f(x+h)−f(x)h=3(x+h)2−2(x+h)+1−(3x2−2x+1)h

Step 3 ：Step 3: Simplify to get 3(x2+2xh+h2)−2x−2h+1−3x2+2x−1h

Step 4 ：Step 4: Combine like terms and simplify further to get 6xh+3h2−2hh

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

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