How do you find the average rate of change of $y = 3 x^{2} - 3$ $y=3x^2-3$ over [-3,3]?

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Answer 1 · 2017-02-27T00:38:58

Zero

In general, the average rate of change of function $f (x)$ $f(x)$ , over an interval $[a, b], i s$ $[a,b], is$ :

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

Here that means:

$\frac{[3 {(3)}^{2} - 3] - [3 {(- 3)}^{2} - 3]}{3 - (- 3)}$ $([3(3)^2 - 3] - [3(-3)^2 - 3])/(3 - (- 3))$

$= \frac{0}{6} = 0$ $= (0)/(6) = 0$

This is hardly surprising as the function is even , ie $f (x) = f (- x)$ $f(x) = f(-x)$ .

How do you find the average rate of change of y=3x2−3y=3x^2-3 over [-3,3]?