Given f(x)=17-x^2 what is the average rate of change in f(x) over the interval [1, 5]? -6 -1/2 1/4 1

choice A) -6



Work Shown:

Plug in x = 1
f(x) = 17-x^2
f(1) = 17-1^2
f(1) = 17-1
f(1) = 16

Then plug in x = 5
f(x) = 17-x^2
f(5) = 17-5^2
f(5) = 17-25
f(5) = -8

So the average rate of change (AROC) from x = 1 to x = 5 is...
AROC = (f(b)-f(a))/(b-a)
AROC = (f(5)-f(1))/(5-1)
AROC = (-8-16)/(5-1)
AROC = (-24)/(4)
AROC = -6

That's why the answer is choice A) -6

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