Given f(x) = 17- x². What is the average rate of change in f(x) over the interval [1, 5]?

Solution:

Given, f(x) = 17 - x²

We have to find the average rate of change in f(x) over the interval (1, 5)

The average rate of change of the function f(x) over the interval (a, b) is equal to

\(\frac{[f(b)-f(a)]}{(b-a)}\)

Here, a = 1 and b = 5

f(1) = 17 - (1)²

f(1) = 17 - 1

f(1) = 16

f(5) = 17 - (5)²

f(5) = 17 - 25

f(5) = -8

Now, to find average rate of change in f(x)

\(\frac{[f(b)-f(a)]}{(b-a)}\) = \(\frac{[(-8)-16]}{(5-1)}\)

= \(\frac{(-8-16)}{4}\)

= -24/4

= -6

Therefore, the average rate of change of the given function over the interval (1, 5) is -6.

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Given f(x) = 17- x². What is the average rate of change in f(x) over the interval [1, 5]?

Summary:

Given f(x) = 17- x². The average rate of change of f(x) over the interval (1, 5) is -6.