Homework SourseDetermine the difference quotient for the following function
Determine the difference quotient for the following function
f(x) = 3x^2-9x+31
Solution
Difference quotient = [ f(x+h) - f(x) ]/ h
f(x+h) = 3(x+h)2 - 9(x+h) + 31
f(x+h) - f(x) = 3(x2 + 2xh + h2) - 9(x+h) + 31 - 3x2-9x-31
=> f(x+h) - f(x) = 3x2 + 6xh + 3h2 - 9x - 9h + 31 - 3x2 - 9x - 31 = 6xh + 3h2 -9h
f(x+h) - f(x) /h = (6xh+3h2-9h)/h = h(6x+3h-9)/h = 6x+3h-9
![Determine the difference quotient for the following function f(x) = 3x^2-9x+31SolutionDifference quotient = [ f(x+h) - f(x) ]/ h f(x+h) = 3(x+h)2 - 9(x+h) + 31](/WebImages/39/determine-the-difference-quotient-for-the-following-function-1120253-1761595995-0.webp "Determine the difference quotient for the following function f(x) = 3x^2-9x+31SolutionDifference quotient = [ f(x+h) - f(x) ]/ h f(x+h) = 3(x+h)2 - 9(x+h) + 31")
