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

Answer:

  3x² +3xh +h²

Step-by-step explanation:

  $\dfrac{f(x+h)-f(x)}{h}=\dfrac{(x+h)^3-x^3}{h}=\dfrac{(x^3+3x^2h+3xh^2+h^3)-x^3}{h}\\\\=\dfrac{3x^2h+3xh^2+h^3}{h}=3x^2+3xh+h^2$