Question

Given f(x)= 7-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

Average rate of change = -6

Explanation:

We have given a function.

f(x)= 7-x²

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

Average rate = f(b)-f(a) / b-a

Let b = 5 and a = 1

f(b) = 7-(5)²

f(b)= 7-25= -18

f(a) = 7-(1)²

f(a) = 7-1

f(a) = 6

Putting values in given formula, we have

Average rate of change = (-18-6) / (5-1)

Average rate of change = -24 / 4

Average rate of change = -6 which is the answer.

Answer 2

-6

Explanation:

The average rate of change is given by

f(x2) - f(x1)

--------------

x2-x1

x2=5 and x1 = 1

f(5) =7 - 5^2 = 7-25 = -18

f(1) = 7-1^2 = 7-1 = 6

-18-6

-----------

5-1

-24

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4

-6