Question

Please Help? For the function f(x) = 2|x – 1|, what is the average rate of change over the interval –1 ≤ x ≤ 1?

Answer 1

Answer:   -2

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Explanation:

Plug in x = -1 to find that

f(x) = 2|x-1|

f(-1) = 2|-1-1|

f(-1) = 2|-2|

f(-1) = 2*(2)

f(-1) = 4

If you repeat for x = 1, you should find that f(1) = 0

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Now use the average rate of change formula below. Effectively, we're using the slope formula more or less.

$m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(1)-f(-1)}{1-(-1)}\\\\m = \frac{0-4}{1+1}\\\\m = \frac{-4}{2}\\\\m = -2$

The average rate of change on this interval is -2

This is the same as finding the slope through the points (-1, 4) and (1, 0).