Question

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

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