Find and simplify the difference quotient f(x+h)-f(x)/h, h cannot equal 0 for the given function. f(x) = 2x^2

Question

Find and simplify the difference quotients. 

Answer 1

f(x) = 2x²

 

[f(x+h) - f(x)]/h = [2(x+h)² - 2x²]/h

 

                         = [2(x²+2xh+h²) - 2x²]/h

 

                         = [4xh + 2h²]/h = h(4x + 2h) / h = 4x + 2h