Question

How do you find the average rate of change of `y=sqrtx` over [0,2]?

Answer 1

The average rate of change of function `f` on interval `[a,b]` is `(f(b) - f(a))/(b-a)`

Explanation:

It is the ratio of the changes, it may also be written `(Deltaf)/(Deltax)` and it may be thought of as the slope of the line through the endpoints of the graph of `f` on the interval.

Algebraically it is (one version of) the difference quotient. (The quotient of the differences in `f` values and `x` values..)

For the function `f(x) = sqrtx` on `[0,2]`, we get

Average rate of change `= (sqrt2 - sqrt0).(2-0) = sqrt2/2`