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Find the difference quotient (f(x+h)-f(x))/(h), where h!=0, for the function below. f(x)=6x-2 Simplify your answer as much as possible.

Find the difference quotient f(x+h)−f(x)h \frac{f(x+h)-f(x)}{h} , where h≠0 h \neq 0 , for the function below.\newlinef(x)=6x−2 f(x)=6 x-2 \newlineSimplify your answer as much as possible.

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Full solution

Q. Find the difference quotient f(x+h)−f(x)h \frac{f(x+h)-f(x)}{h} , where h≠0 h \neq 0 , for the function below.\newlinef(x)=6x−2 f(x)=6 x-2 \newlineSimplify your answer as much as possible.
  1. Substitute into formula: Substitute f(x)f(x) and f(x+h)f(x+h) into the difference quotient formula.\newlinef(x)=6x−2f(x) = 6x - 2\newlinef(x+h)=6(x+h)−2=6x+6h−2f(x+h) = 6(x+h) - 2 = 6x + 6h - 2
  2. Plug into difference quotient: Plug f(x+h)f(x+h) and f(x)f(x) into the difference quotient.\newline(f(x+h)−f(x)h=(6x+6h−2)−(6x−2)h)(\frac{f(x+h) - f(x)}{h} = \frac{(6x + 6h - 2) - (6x - 2)}{h})
  3. Simplify numerator: Simplify the numerator. (6x+6h−2−6x+2)/h=(6h)/h(6x + 6h - 2 - 6x + 2) / h = (6h) / h
  4. Cancel hh in expression: Simplify the expression by canceling hh in the numerator and the denominator.6hh=6\frac{6h}{h} = 6

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