Answer:
The average rate of change for g(x) on the interval 3 ≤ x ≤ 6 is -1.
Step-by-step explanation:
We want to find the average rate of change of the function:
[tex]g(x)=x^2-10x+19[/tex]
Over the interval:
[tex]3\leq x\leq 6[/tex]
The average rate of change is essentially the average slope of the function. So, we want to find the slope between g(3) and g(6).
Evaluate both points:
[tex]g(3)=(3)^2-10(3)+19=-2[/tex]
[tex]g(6)=(6)^2-10(6)+19=-5[/tex]
Thus, we obtain the two points (3, -2) and (6, -5).
The slope between them is:
[tex]\displaystyle m=\frac{(-5)-(-2)}{(6)-(3)}=\frac{-3}{3}=-1[/tex]
Therefore, the average rate of change for g(x) on the interval 3 ≤ x ≤ 6 is -1.
