Question

What is the average rate of change for the functionf(x)=3x²-5 on the interval -3≤x ≤-1

Answer 1

The average rate of change for the function between the given interval is;

`-12`

Step-by-step explanation:

The average rate of change for the given function;

`f(x)=3x^2-5`

Between the interval;

`-3\leq x\leq-1`

can be calculated as;

`\Delta f(x)=(f(-1)-f(-3))/(-1-(-3))=(f(-1)-f(-3))/(2)`

The value of f(x) at x=-1 and -3 are;

`\begin{gathered} f(-1)=3(-1)^2-5=-2 \\ f(-3)=3(-3)^2-5=27-5=22 \end{gathered}`

So;

`\begin{gathered} \Delta f(x)=(f(-1)-f(-3))/(2)=(-2-22)/(2)=-(24)/(2) \\ \Delta f(x)=-12 \end{gathered}`

Therefore, the average rate of change for the function between the given interval is;

`-12`