Answer:
The average rate of change is -75
Step-by-step explanation:
The Average Rate of Change (ARC)
It's a measure of how much the function changed per unit, over a given interval.
Given a function F(x) and an interval between x=a and x=b, the average rate of change is:
[tex]\displaystyle A=\frac{F(b)-F(a)}{b-a}[/tex]
The function is:
[tex]F(x)=-x^3+24x^2-179x+495[/tex]
and it's required to find the ARC between x=2 and x=5.
Calculate F(2) and F(5):
[tex]F(2)=-2^3+24*2^2-179*2+495=225[/tex]
[tex]F(5)=-5^3+24*5^2-179*5+495=75[/tex]
The ARC is:
[tex]\displaystyle A=\frac{75-225}{5-3}=\frac{-150}{2}=-75[/tex]
The average rate of change is -75
