Find the average rate of change for the interval specified?

Question

f (x) = 2x^2 + 1  on [x, x+h]

Answer 1

Avg rate of change = [f(x+h) - f(x)]/[x+h-x]

 

                            = [2(x+h)² + 1 - (2x² + 1)]/h

 

                            = [2(x²+2xh+h²)+1-2x²-1]/h

 

                            = (4xh+2h²)/h

 

                            = h(4x+2h)/h  = 4x+2h