Find the average rate of change of each function on the interval specified for real numbers b or h. f(x) = 2x^2 + 1 on [x, x + h]

Answer 1

A.R.o.c = [f(x+h) - f(x)] / [ x+h - x ] =

[f(x+h) - f(x)] / h]

f(x+h) = 2(x+h)^2 + 1 = 2(x^2+ 2xh + h^2) + 1 = 2x^2 + 4xh + 2h^2 + 1

f(x+h) - f(x) = 2x^2 + 4xh + 2h^2 + 1 - 2x^2 - 1

= 4xh + 2h^2

Dividing by h:

4x + 2h

The denominator is just