Question

Find the intervals in which the function $f$ given by $f\left(x\right)=x^2-4x+6$ is
i) Strictly increasing
ii) Strictly decreasing

Answer 1

Given function is $f\left(x\right)=x^2-4x+6$

Now differentiate given equation w.r.t $x$, we get

$f^{\prime }\left(x\right)=2x-4$

For the function to be strictly increasing, $f^{\prime }\left(x\right)$ must be greater than zero.

$⟹f^{\prime }\left(x\right)=2x-4>0$

$⟹x>2$ i.e $x\in (2,\infty )$

For the function to be strictly decreasing , $f^1\left(x\right)$ must be less than zero.

$⟹f^{\prime }\left(x\right)=2x-4<0$

$⟹x<2$ i.e. $x\in (-\infty ,2)$