Question

How do you find the average rate of change of `h(x) = x^3 − 1/5e^x` from [0,1]?

Answer 1

`(6-e)/5`

Explanation:

(Average Rate of Change)`=(h(1)-h(0))/(1-0)=1-e/5-(0-1/5)=(6-e)/5`

I hope that this was clear.

Answer 2

`1/5(6-e)`

Explanation:

`"the average rate of change is given by"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((h(b)-h(a))/(b-a))color(white)(2/2)|)))`
`"where the interval is " [a,b]`

`h(b)=h(1)=1-1/5e`

`h(a)=h(0)=-1/5`

`rArr(1-1/5e+1/5)/1=1/5(6-e)`