Question

for each problem, a quadratic function g has the given

1. avg rate of change is 1 on the interval $-3 \leq x \leq 0$.

avg rate of change is 5 on the interval $0 \leq x \leq 3$.
what is the average rate of change of g on the interval
$3 \leq x \leq 6$?
\boxed{9}
the rate of change of the average rate of change of a
quadratic function is constant for equal length
intervals. for this problem, the avg rate of change is
increasing by 4 for each interval of 3.

Explanation:

Step1: Analyze interval lengths

All intervals (\(-3\leq x\leq0\), \(0\leq x\leq3\), \(3\leq x\leq6\)) have length \(3 - 0=3\), \(0 - (-3)=3\), \(6 - 3 = 3\) (equal length).

Step2: Find the rate of increase

From \(-3\leq x\leq0\) (avg rate = 1) to \(0\leq x\leq3\) (avg rate = 5), the increase is \(5 - 1 = 4\). So, the average rate of change increases by 4 per 3 - unit interval.

Step3: Calculate the rate for \(3\leq x\leq6\)

For \(0\leq x\leq3\), avg rate is 5. Add the increase (4) to get the rate for \(3\leq x\leq6\): \(5+4 = 9\).

Answer:

9