State when a function `f(x)` is said to be increasing on an interval `[a ,\ b]` . Test whether the function `f(x)=x^2-6x+3` is increasing on the interval `[4,\ 6]` .

Explanation

We have given

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

`implies f′(x)=2(x−3)`

Now, `x in [4,6] implies x`>`3`

`implies 2(x−3)`>`0`

`implies f′(x)`>`0`

So, `f(x)` is increasing on `[4,6]`