Question

How do you find the average rate of change of `g(x)=2x^3-4x^2` between x=1 and x=3?

Answer 1

10

Explanation:

The average rate of change is calculated using

`color(red)(|bar(ul(color(white)(a/a)color(black)( (g(b) - g(a))/(b - a))color(white)(a/a)|)))`

here a = 1 and b = 3

`g(3) = 2(3)^3 - 4(3)^2 = 54 - 36 = 18`

and `g(1) = 2(1)^3 - 4(1)^2 = 2-4 = -2`

`rArr " average rate of change " = (18-(-2))/(3-1) = 20/2 = 10`