Find the intervals in which the function $f$ given by $f(x)=x^2−4x+6$ is (a) strictly increasing (b) strictly decreasing

The correct answer is (a) strictly increasing in interval $(2,∞)$
(b) strictly decreasing in the interval $(−∞,2)$

$f(x)=x^2−4x+6$

Differentiate $f'(x)=2x−4$

$f'(x)=0 ⇒ 0=2x−4 ⇒ x=2$


The point $x=2$ divides the curve into two disjoint intervals namely $(−∞,2)$ and $(2,∞)$


In the interval $(−∞,2)$, $f'(x)=2x−4<0$

Hence, $f$ is strictly decreasing in $(−∞,2)$


In the interval $(2,∞)$, $f'(x)>0$

Hence, in the interval $(2,∞)$, the function f is strictly increasing.