Question

Find the intervals in which the function $f\left(x\right)=x^2-4x+6$ is strictly decreasing.

Answer 1

A function $f\left(x\right)$ is said to be strictly decreasing if $\frac{d\left(f\right(x\left)\right)}{dx}<0$

Now, $f\left(x\right)=x^2-4x+6$ is decreasing

if $\frac{d\left(f\right(x\left)\right)}{dx}<0$

i.e. if $2x-4<0$

i.e. if $x<2$

Hence, $f\left(x\right)$ is decreasing for $x\in (-\infty ,2)$