Question

which is the best estimate of the average rate of change for the function given in the table, over the interval 1 ≤ x ≤ 3? a 6 b 12 c 16 d 24

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\).

Step2: Identify \(a\), \(b\), \(f(a)\) and \(f(b)\)

Here, \(a = 1\), \(b=3\). From the table, when \(x = 1\), \(y=f(1)=5\) and when \(x = 3\), \(y = f(3)=29\).

Step3: Substitute values into the formula

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Answer:

B. 12