Answer:
4
Step-by-step explanation:
Let the function given be f(x) = x³
The formula for calculating the average rate of change is expressed by:
f'(x) = [tex]\frac{f(x+h)-f(x)}{h}[/tex]
If f(x) = x³
f(x+h) = (x=h)³
substitute the functions in the formula
[tex]f'(x) = \frac{(x+h)^3-x^3}{h}\\f'(x) = \frac{(x^3+3xh^2+3hx^2+h^3)-x^3}{h}\\f'(x) = \frac{3xh^2+3hx^2+h^3}{h}\\f'(x) = \frac{h(3xh+3x^2+h^2)}{h}\\f'(x) = 3xh+3x^2+h^2[/tex]
Since h = x₂-x₁ and x = 0
[tex]f'(x) = 3(0)(2-0)+3(0)^2+(2-0)^2\\f'(x) = 0+0+2^2\\f'(x) = 4\\[/tex]
Hence the average rate of change is 4
