Question

Write down the range of `f(x)=x^2-6x+10` for `-3<x<8`?. thanks

Answer 1

`1<=f(x)<37`

Explanation:

First, we find the minimum point the graph reaches by differentiationg and making that equal .

`f(x)=x^2-6x+10`
`f'(x)=2x-6=0`
`x=3`

The minimum point occurs at `x=3` which is in the given domain, `f(3)=3^2-6(3)+10=1`

For the maximum, we just put in `8` and `-3`, `f(8)=8^2-6(8)+10=26`; `f(-3)=(-3)^2-6(-3)+10=37`

`1<=f(x)<37`