Question

Given ix) = 17 - x2, what is the average rate of change in f(x) over the interval [1, 5]?

Answer 1

Answer:   -6

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Explanation:

Plug in x = 1

f(x) = 17-x^2

f(1) = 17-1^2

f(1) = 17-1

f(1) = 16

Repeat for x = 5 to find that f(5) = -8

Now we'll use the formula below to find the average rate of change from x = a to x = b.

$m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(5)-f(1)}{5-1}\\\\m = \frac{-8-16}{4}\\\\m = \frac{-24}{4}\\\\m = -6$

The average rate of change is -6

The formula is basically the slope formula, more or less. So that's why I used 'm' to represent the average rate of change.

The average rate of change on the interval [1,5] is the same as finding the slope through the lines (1, 16) and (5, -8)