Question

what is the average rate of change of g(x) on the interval [1,3]

g(x)=x^2-1

Answer 1

The average rate of change of the function g(x) on the interval [1,8] is [g(8) - g(1)] / (8 - 1) = (1/7) [g(8) - g(1)].

In general, the average value of a function f(x) on an interval [a,b] is Integral[f(x),x,a,b] / (b - a). If f(x) = dg(x)/dx, Integral[dg(x)/dx,x,a,b]/(b - a) = [g(b) - g(a)] / (b - a).

Or, think about it in terms of velocity. The average velocity of a particle with position x(t) from t = t1 to t2 is [x(t2) - x(t1)] / (t2 - t1).

Answer 2

pellet, 1,3?

Answer 3

not a big deal to just change the bounds