Question

Find the rate of change for x³. You need to work out the change in f(x)=x³ when x is increased by a small number h to x+h. So you will work out f(x+h)-f(x). Then do some algebra to simplify this. Then divide this by h to get the average rate of change of f(x) between x and x+h. The average rate of change of f(x) from x to x+h is:

Answer 1

3x² +3xh +h²

Explanation:

`(f(x+h)-f(x))/(h)=((x+h)^3-x^3)/(h)=((x^3+3x^2h+3xh^2+h^3)-x^3)/(h)\\\\=(3x^2h+3xh^2+h^3)/(h)=3x^2+3xh+h^2`