find the average rate of change for the given interval. 1 ≤ x ≤ 6

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 6$, $f(1)=200$, and $f(6)=350$.

Step2: Substitute values into the formula

$\frac{f(6)-f(1)}{6 - 1}=\frac{350 - 200}{6 - 1}$.

Step3: Calculate the result

$\frac{350 - 200}{6 - 1}=\frac{150}{5}=30$.

Answer:

$30$