Question

Consider the function `y=-x^2+4`. What is the average rate of change from `[1, 5]`?

Answer 1

`-6`

Explanation:

The average rate of change of a continuous function,
`f(x)` , on a closed interval `[a,b]` is given by

`bar f(x) =(f(b)-f(a))/(b-a)`

So the average rate of change of the function `f(x)=-x^2+4` on `[1,5]` is:

`Aroc = ( f(5)-f(1) ) / ( 5-1 )`
`" " = ( ( -25+4) - (-1+4) ) / 4`
`" " = ( ( -21) - (3) ) / 4`
`" " = -24/4`
`" " = -6`