Question

How do you find the average rate of change of `y = 9x^3 - 2x2 + 6` over interval [-4,2]?

Answer 1

`112`

Explanation:

`"the average rate of change of y over a closed interval"`
`[a,b]" is a measure of the slope of the secant connecting"`
`"the 2 points and is calculated using"`

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

`"here "[a,b]=[-4,2]`

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

`color(white)(xxxxxxxx)=72-8+6=70`

`f(a)=f(-4)=9(-4)^3-2(-4)^2+6`

`color(white)(xxxxxxxxxx)=-576-32+6=-602`

`"average rate of change "=(70-(-602))/(2-(-4))`

`color(white)(xxxxxxxxxxxxxxxx)=672/6=112`