Question

Help! What is the average rate of change of f(x)=x^2+3x+6 over the interval -3 less-than-or-equal-to x less-than-or-equal-to 3?

Answer 1

The average rate of change of the function over the interval is 5.

Explanation:

Average rate of change of a function:

The average rate of change of a function f(x) over an interval [a,b] is given by:

`A = (f(b)-f(a))/(b-a)`

Interval -3 less-than-or-equal-to x less-than-or-equal-to 3

This means that
`a = -3, b = 3`

`f(x) = x^2 + 3x + 6`

So

`f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24`

`f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6`

Average rate of change

`A = (f(b)-f(a))/(b-a) = (24+6)/(3-(-3)) = (30)/(6) = 5`

The average rate of change of the function over the interval is 5.