Question

Find the intervals in which the function f given by $f\left(x\right)=x^2-6x+5$ is
(a) Strictly increasing
(b) Strictly decreasing

Answer 1

Given :

$f\left(x\right)=x^2-6x+5$

Finding domain of $f\left(x\right):$

$\Rightarrow f\left(x\right)=0;$

${\Rightarrow x}^2-5x-x+5=0$

$\Rightarrow x(x-5)-1(x-5)=0$

$\Rightarrow (x-5)(x-1)=0$

$\Rightarrow x=5,1$

Required intervals becomes $(-\infty ,1],(1,5],(5,\infty )$.

Now, checking increasing and decreasing regions

$\Rightarrow f^{{}^{\prime }}\left(x\right)=2x-6$