Question

If $-4\le x\le 4$, then critical points of $f\left(x\right)=x^2-6\left|x\right|+4$ are

• A. $3,-2$
• B. $6,-6$
• C. $3,-3,0$
• D. $0,1,3$

Answer 1

The correct option is C $3,-3,0$

For $x\ge 0$:

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

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

For critical point $f^{\prime }\left(x\right)=0$

Hence $x=3$

For $x\le 0$:

$f\left(x\right)=x^2+6x+4$

$f^{\prime }\left(X\right)=2x+6$

For critical point $f^{\prime }\left(x\right)=0$

Hence $x=-3$

Also the curve is similar about line $x=0$ i.e. $y-axis$

Hence function have a critical point at $x=0$

So the critical points are $0,3,-3$