find the average rate of change over 0,3 for the function ( f(x)=x^{2}+4 )

Answer

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}). Here (a = 0), (b=3), and (f(x)=x^{2}+4).

Step2: Calculate (f(0)) and (f(3))

For (x = 0): (f(0)=0^{2}+4=4).
For (x = 3): (f(3)=3^{2}+4=9 + 4=13).

Step3: Substitute into the formula

(\frac{f(3)-f(0)}{3-0}=\frac{13 - 4}{3}=\frac{9}{3}=3).

Answer:

D. 3