Question

Help Pre-Calc

Fill in the blank question :

Calculate the average rate of change f(x) over the interval (-4,-1) using the formula ___________. The value of f(-1) is ____. The value of f(-4) is ____. The average rate of change of f(x) over the interval (-4,-1) is ____.

Answer 1

Average rate of change = 2

Explanation:

We need to find the average rate of change of f(x) over the interval [-4,-1], so first we need to find the end points at x=-4 and x=-1.

From graph we see that y=-3 when x=-4, So the point is (-4,-3)

From graph we see that y=3 when x=-1, So the point is (-1,3)

Now we can plug these points into average rate of change formula:

`Average\ rate=(f\left(b\right)-f\left(a\right))/(b-a)`

where (a,f(a)) and (b,f(b)) are the given points.

`Average\ rate=(-3-3)/(-4-\left(-1\right))`

`Average\ rate=(-3-3)/(-4+1)`

`Average\ rate=(-6)/(-3)`

`Average\ rate=2`

Hence final answer is 2.