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Find the difference quotient (f(x+h)-f(x))/(h), where h!=0, for the function below. f(x)=8x-5 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)=8x−5 f(x)=8 x-5 \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)=8x−5 f(x)=8 x-5 \newlineSimplify your answer as much as possible.
  1. Calculate f(x+h)f(x+h): Calculate f(x+h)f(x+h) for the function f(x)=8x−5f(x) = 8x - 5.\newlinef(x+h)=8(x+h)−5=8x+8h−5f(x+h) = 8(x+h) - 5 = 8x + 8h - 5.
  2. Substitute into formula: Substitute f(x+h)f(x+h) and f(x)f(x) into the difference quotient formula.\newline(f(x+h)−f(x)h=(8x+8h−5)−(8x−5)h)(\frac{f(x+h) - f(x)}{h} = \frac{(8x + 8h - 5) - (8x - 5)}{h}).
  3. Simplify numerator: Simplify the numerator by combining like terms.\newline(8x+8h−5−8x+5)/h=(8h)/h(8x + 8h - 5 - 8x + 5) / h = (8h) / h.
  4. Cancel hh in expression: Simplify the expression by canceling hh in the numerator and the denominator.8hh=8\frac{8h}{h} = 8.

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