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

Explanation

`f(x)=x^{2}-6 x+3`
`
f^{prime}(x)=2 x-6`
`
Rightarrow f^{prime}(x)=2(x-3) `
`
Now, f^{prime}(4)=2(4-3) `
`
=2`
`
f^{prime}(4)>0`

So, f(x) is increasing on `x=4`
`
. f^{prime}(6)=2(6-3) `
`
...