Calculate the average rate of change of f(x) = (x²/4) - 5 for 3 ≤ x ≤ 5.

Solution:

Given: Function f(x) = (x²/4) - 5 and the interval is 3 ≤ x ≤ 5

The average rate of change of any function f over interval [a,b]is defined as

[f(b) - f(a)]/[b - a]

So, you need to find [f(5) - f(3)]/[5 - 3]

f(5) = (5²/4) - 5

=(25/4 - 5) = 5/4

f(3)= (3²/4) - 5

=(9/4 - 5)= -11/4

[f(b) - f(a)]/[b - a] = {5/4+11/4}/[5 - 3]

=[16/4]/2

= 4/2

= 2

Therefore, the average rate of change of a given function is 2.

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Calculate the average rate of change of f(x) = (x²/4) - 5 for 3 ≤ x ≤ 5.

Summary:

The average rate of change of f(x) = (x²/4) - 5 for 3 ≤ x ≤ 5 is 2.