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:

f(x) = 17 - x^2
f(1) = 17 - (1)^2
f(1) = 17 - 1
f(1) = 16
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f(x) = 17 - x^2
f(5) = 17 - (5)^2
f(5) = 17 - 25
f(5) = -8
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m = (f(b) - f(a))/(b - a)
m = (f(5) - f(1))/(5 - 1)
m = (-8 - 16)/(5 - 1)
m = (-24)/(4)
m = -6

Answer 2

Average rate of change is -6

Explanation:

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

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

use formula Average =
`(f(b)-f(a))/(b-a)`

Given interval is [1, 5] a=1, b=5

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

`f(1)=17-1^2=16`

`f(5)=17-5^2=-8`

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

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

=
`(-24)/(4)=-6`

Average rate of change is -6