Answer:
Average rate of change: [tex]-3[/tex]
Step-by-step explanation:
Remember:
The average rate of change of a function over an interval [tex][a,b][/tex] is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given:
[tex][a,b]=[1,7][/tex]
[tex]f(b)=f(7)[/tex]
[tex]f(a)=f(1)[/tex]
Calculation:
[tex]f(b)=f(7)=-(7)^2+5(7)+14=-49+35+14=-49+49=0[/tex]
[tex]f(a)=f(1)=-(1)^2+5(1)+14=-1+5+14=4+14=18[/tex]
[tex]\frac{f(b)-f(a)}{b-a}=\frac{0-18}{7-1}=\frac{-18}{6}=-3[/tex]
Therefore, the average rate of change of the function [tex]g(x)=-x^2+5x+14[/tex] over the interval [tex]1\leq x\leq7[/tex] is [tex]-3[/tex].
