Question

Please help me! And please no scam answers

Answer 1

Average rate of change:
`-3`

Explanation:

Remember:

The average rate of change of a function over an interval
`[a,b]` is
`(f(b)-f(a))/(b-a)`

Given:

`[a,b]=[1,7]`

`f(b)=f(7)`

`f(a)=f(1)`

Calculation:

`f(b)=f(7)=-(7)^2+5(7)+14=-49+35+14=-49+49=0`

`f(a)=f(1)=-(1)^2+5(1)+14=-1+5+14=4+14=18`

`(f(b)-f(a))/(b-a)=(0-18)/(7-1)=(-18)/(6)=-3`

Therefore, the average rate of change of the function
`g(x)=-x^2+5x+14` over the interval
`1\leq x\leq7` is
`-3`.