Question

The average rate of change of f(x) is given by the formula f(7) - f (3) 4. Over what interval does this formula give the average rate of change for f(x)?

Answer 1

The answer would be 4

Answer 2

The interval over which this formula give the average rate of change for f(x) is:

[3,7]

Explanation:

We know that when we are asked to find the average rate of change of the function f(x) over the interval [a,b] then the formula for the average rate of change is given by:

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

Here we have:

a=3 and b=7

Hence, the average rate of change is:

`\text{Rate\ of\ change}=(f(7)-f(3))/(7-3)`

i.e.

`\text{Rate\ of\ change}=(f(7)-f(3))/(4)`

Hence, the interval is: [3,7]