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].

Explanation:

It is given that,

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

The average rate of change is given by,

$Average\text{ }rate\text{ }of\text{ }change=\frac{f(b)-f(a)}{b-a}$

That implies,

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

Also,

$\begin{gathered} f(-2)=(-2)^^2+10 \\ =4+10 \\ =14 \end{gathered}$

Therefore,

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

Hence, the average rate of change is -3.