Question

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

Answer 1

Answer:

The average rate of change is -6.

Step-by-step explanation:

Given function is,

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

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

$m=\frac{f(5)-f(1)}{5-1}$

$=\frac{(17-5^2)-(17-1^2)}{4}$   ( From equation (1) )

$=\frac{(17-25)-(17-1)}{4}$

$=\frac{-8-16}{4}$

$=\frac{-24}{4}$

$=-6$

Hence, first option is correct.

Answer 2

Answer: 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