Question

find the average rate of change over 0,2 for the function $f(x)=x^{2}+4$

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\), \(b=4\), and \(f(s)=s^{2}+4\).

Step2: Calculate \(f(4)\) and \(f(0)\)

• For \(s = 4\), \(f(4)=4^{2}+4=16 + 4=20\).
• For \(s = 0\), \(f(0)=0^{2}+4=4\).

Step3: Apply the average - rate - of - change formula

\(\frac{f(4)-f(0)}{4-0}=\frac{20 - 4}{4}=\frac{16}{4}=4\).

Answer:

4