Question

the average rate of change for the interval $2\leq x \leq 3.5$ is

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $f(x)$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$

Step2: Identify values from the graph

Let $a=2$, $f(a)=2.333$; $b=3.5$, $f(b)=-4.79$

Step3: Substitute into the formula

$\frac{-4.79 - 2.333}{3.5 - 2}$

Step4: Calculate numerator and denominator

Numerator: $-4.79 - 2.333 = -7.123$
Denominator: $3.5 - 2 = 1.5$

Step5: Compute the final value

$\frac{-7.123}{1.5} \approx -4.749$

Answer:

$-4.75$ (rounded to two decimal places, or $-4.749$ for more precision)