How do you find the average rate of change of $f (x) = 2 x^{2} + 2$ $f(x)=2x^2+2$ from 4 to 6?

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Answer 1 · 2016-03-12T13:53:42

$20$ $20$ (details in "Explanation")

For a function $f (x)$ $f(x)$ the rate of change, in a close interval $a \to b$ $a to b$ , is given by

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

For
$f (x) = 2 x^{2} + 2$ $f(x) = 2x^2+2$
The required rate of change (with $a = 4 and b = 6$ $a=4 and b=6$ ) is

$\frac{[2 \cdot 6^{2} + 2] - [2 \cdot 4^{2} + 2]}{6 - 4}$ $([2*6^2+2]-[2*4^2+2])/(6-4)$
$\frac{74 - 34}{2} = \frac{40}{2} = 20$ $(74-34)/2=40/2=20$

How do you find the average rate of change of f(x)=2x2+2f(x)=2x^2+2 from 4 to 6?