determine the average rate of change of f(x)=x^2 + 4x - 5 on the interval 1,3.

Answer:

$8$

Explanation:

Step1: Recall the average rate of change formula

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

Step2: Calculate (f(1)) and (f(3))

For (x = 1), (f(1)=1^{2}+4\times1 - 5=1 + 4-5=0). For (x = 3), (f(3)=3^{2}+4\times3 - 5=9 + 12-5 = 16).

Step3: Substitute into the formula

(\frac{f(3)-f(1)}{3 - 1}=\frac{16-0}{2}=\frac{16}{2}=8).