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

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

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

Answer

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