the average rate of change for the interval 2 ≤ x ≤ 3.5 is

Explanation:

Step1: Recall average - rate - of - change formula

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, $a = 2$, $b=3.5$, $f(2)=2.333$ and $f(3.5)=- 4.79$.

Step2: Substitute values into formula

$\frac{f(3.5)-f(2)}{3.5 - 2}=\frac{-4.79 - 2.333}{3.5 - 2}$.

Step3: Calculate the numerator and denominator

The numerator is $-4.79-2.333=-7.123$, and the denominator is $3.5 - 2 = 1.5$.

Step4: Compute the result

$\frac{-7.123}{1.5}\approx - 4.75$.

Answer:

$-4.75$