Question

Find the average rate of change of the function

f
(
x
)
=

−
1
x
2
−
2
x
+
2
, on the interval
x
∈
[3,5].

Answer 1

The average rate of change is −10.

Explanation:

The average rate of change of f(x) on the interval [a,b] is f(b) − f(a) / b−a.

We have, a=3, b=5, f(x) = -1x^2 − 2x + 2.

Thus, f(b) − f(a) = −(5)^2 −2(5) + 2 − [−(3)^2 −2(3) + 2]

= -25 - 10 + 2 - ( -9 - 6 + 2 )

= -33 - 13

= - 20

Then, b−a = 5 - 3 = 2

f(b) − f(a) / b−a = - 20 / 2 = −10

Answer: the average rate of change is −10.