Question

What is the average rate of change of the function from x1 to x2? f(x) = -3x^2 - x from x1 = 5 to x2 = 6

Answer 1

`color(blue)(-34)`

Explanation:

The average rate of change over an interval `[a,b]` is given as:

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

Given function is:

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

Given interval is:

`[5,6]`

`f(6)=-3(6)^2-6=-114`

`f(5)=-3(5)^2-5=-80`

Average rate of change:

`(-114-(-80))/(6-5)=-34`