Question

Given the tunction

f(x)= - x^2 + 4x - 3 ,find the rate of chango over the interval [-2,7] (you can take the negative leading coefficlent off for reg ed if you want) *

Answer 1

-1

Explanation:

Given function:
`f(x)=-x^2+4x-3`

`\implies f(-2)=-(-2)^2+4(-2)-3=-15`

`\implies f(7)=-(7)^2+4(7)-3=-24`

`\textsf{Average rate of change}=(f(b)-f(a))/(b-a)\quad\textsf{for}\:a\leq x\leq b`

Therefore, average rate of change over the interval -2 ≤ x ≤ 7

`\implies \textsf{Average rate of change}=(f(7)-f(-2))/(7-(-2))=(-24-(-15))/(9)=-1`