Question

F(x) = x2 + 10х=What is the average rate of change of fover the interval [-2, -1]?

Answer 1

Given

`f(x)=x^2+10`

To find the average rate of change of f over the interval [-2,-1].

Step-by-step explanation:

It is given that,

`f(x)=x^2+10`

The average rate of change is given by,

`Average\text{ }rate\text{ }of\text{ }change=(f(b)-f(a))/(b-a)`

That implies,

`\begin{gathered} f(-1)=(-1)^2+10 \\ =1+10 \\ =11 \end{gathered}`

Also,

Therefore,

`\begin{gathered} Average\text{ }rate\text{ }of\text{ }change=(f(-1)-f(-2))/(-1+2) \\ =(11-14)/(1) \\ =-3 \end{gathered}`

Hence, the average rate of change is -3.