Question

What is the average rate of change over the interval [-1,4] ​

Answer 1

The average rate of change over the interval [-1,4] ​is 7/5 or 1.4

Explanation:

We need to find average rate of change over the interval [-1,4] ​

The formula used to calculate average rate of change is:
`Average \ rate \ of \ change=(f(b)-f(a))/(b-a)`

We have a= -1 and b = 4

Now finding f(a) and f(b)

Looking at the graph if we have x=-1 i.e f(-1) we get y = -7

So, f(-1) = -7

Now, Looking at the graph if we have x=4 i.e f(4) we get y = 0

So, f(4) = 0

Now, putting values and finding average rate of change

`Average \ rate \ of \ change=(f(b)-f(a))/(b-a)\\Average \ rate \ of \ change=(0-(-7))/(4-(-1))\\Average \ rate \ of \ change=(0+7)/(4+1)\\ Average \ rate \ of \ change=(7)/(5)\\Average \ rate \ of \ change=1.4`

So, The average rate of change over the interval [-1,4] ​is 7/5 or 1.4