Determine the values of `x` for which the function `f(x)=x^2-6x+9` is increasing or decreasing. Also, find the coordinates of the point on the curve `y=x^2-6x+9` where the normal is parallel to the line `y=x+5` .

Explanation

Given as `f(x) = x^2 – 6x + 9`

` ⇒ f'(x) = (d/dx)(x^2 – 6x + 9)`

` ⇒ f’(x) = 2x – 6 `

`⇒ f’(x) = 2(x – 3)`

For the function `f(x)` let us find critical point, we must have

`⇒ f’(x) = 0 ⇒ 2(x – 3) = 0 ⇒ (x – 3) = 0 ⇒ x = 3`


It is clear, `f’(x) > 0` if `x > 3` and `f’(x) < 0` if `x < 3`
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