How do you find the average rate of change for the function f(x)=x3+2x2+x on the indicated intervals [-1,2]?

Question

wyjadaczeqa8 · Accepted Answer

The rate of change is the ratio of the change of one quantity divided by the change of another.
Average rate of change of a function f(x) (with respect to x) is the change in f(x)
divided by the change in x, so
Average rate of change of a function f(x) on an interval [a,b] is:

\frac{f (b) - f (a)}{b - a}

In this question: the function is

f (x) = x^{3} + 2 x^{2} + x

and the interval is
[a,b]=[-1,2]
So the average rate of change of f on the interval is:

\frac{f (2) - f (- 1)}{2 - (- 1)} = \frac{18 - 0}{2 + 1} = \frac{18}{3} = 6

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If we had units for x and f(x) we would use them as f units per x unit

How do you find the average rate of

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