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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

User Lepton
by
7.6k points

2 Answers

3 votes
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
User Aquatic
by
8.1k points
3 votes

Answer:

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

User Isotopp
by
8.0k points

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