Question

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

Answer 1

Answer: choice A) -6

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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

Answer 2

The average rate of change is -6.

Explanation:

Given function is,

`f(x)=17-x^2-----(1)`

Thus, the average rate of change in f(x) over the interval [1, 5],

`m=(f(5)-f(1))/(5-1)`

`=((17-5^2)-(17-1^2))/(4)` ( From equation (1) )

`=((17-25)-(17-1))/(4)`

`=(-8-16)/(4)`

`=(-24)/(4)`

`=-6`

Hence, first option is correct.