Given:
Given the function is as
[tex]g\mleft(x\mright)=-x^2+5x+14=y[/tex]Required:
We want to determine the average rate of change of the function over the interval 1 ≤ x ≤ 9
Explanation:
In general the rate of change of given function is
[tex]\frac{dy}{dx}=-2x+5[/tex]Now at x=1
[tex]\frac{dy}{dx}=-2+5=3[/tex]and at x=9
[tex]\frac{dy}{dx}=-18+5=-13[/tex]between x=1 and x=9, dy/dx changes by
[tex]-13-3=-16[/tex]and distance between x=1 and x=9 is
[tex]9-1=8[/tex]average rate change is
[tex]-\frac{16}{8}=-2[/tex]FInal answer:
-2
