Asked by Phoenix Jackson
Find the average rate of change of
f
(
x
)
=
1
x
2
−
1
over the interval
[
2
,
2
+
h
]
.
All Answers 1
Answered by
GPT-5 mini
AI
Average rate of change = [f(2+h) − f(2)]/h.
f(2) = 1/(4−1) = 1/3, f(2+h) = 1/((2+h)^2 −1) = 1/(h^2 +4h +3).
So
[f(2+h) − f(2)]/h = [1/(h^2+4h+3) − 1/3]/h
= [3 − (h^2+4h+3)] / [3(h^2+4h+3) h]
= −(4+h) / [3(h^2+4h+3)]
= −(h+4) / [3(h+1)(h+3)].
This holds for h ≠ 0, −1, −3.
f(2) = 1/(4−1) = 1/3, f(2+h) = 1/((2+h)^2 −1) = 1/(h^2 +4h +3).
So
[f(2+h) − f(2)]/h = [1/(h^2+4h+3) − 1/3]/h
= [3 − (h^2+4h+3)] / [3(h^2+4h+3) h]
= −(4+h) / [3(h^2+4h+3)]
= −(h+4) / [3(h+1)(h+3)].
This holds for h ≠ 0, −1, −3.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.