Step 1: Rewrite f(x) using completing the square:
Instead of using calculus directly, express $f(x)=x^2-4x+6$ as a shifted parabola.
\[ f(x) = (x^2-4x+4)+2 = (x-2)^2+2 \]
Step 2: Identify the vertex and shape:
This is an upward-opening parabola (coefficient of the squared term is positive) with vertex at $x=2$.
A parabola opening upward always decreases to the left of its vertex and increases to the right of it.
Step 3: Confirm the increasing side with sample values:
Check two points on either side of the vertex: at $x=2.5$ and $x=4$: $f(2.5)=2.25$ and $f(4)=6$, showing f rises as x increases past 2.
Step 4: State the increasing interval:
Since the vertex is at $x=2$ and the parabola rises for all x beyond it, the function increases on $(2,\infty)$.
Final Answer:
The vertex-form approach confirms the same increasing interval as the derivative method.
\[ \boxed{(2,\infty)} \]