Question

If $f\left(x\right)=|x^2-5x+6|$, then $f^{\prime }\left(x\right)$ equals

• A. $2x-5$ for $2<x<3$
• B. $5-2x$ for $2<x<3$
• C. $2x-5$ for $x>2$
• D. $5-2x$ for $x<3$

Answer 1

The correct option is A $2x-5$ for $2<x<3$

$f\left(x\right)=|x^2-5x+6|$, $f^{\prime }\left(x\right)=?$

$f\left(x\right)=|(x-2)(x-3)|$

$f\left(1\right)=|1-5+6|=2$

So in $(2,3)$ it is negative

$\Rightarrow f\left(x\right)=(5x-x^2+6)$ in $(2,3)$

$f^{\prime }\left(x\right)=5-2x$ for $(2<x<3)$.