Question

The shortest distance of the point $(\frac{1}{2},1)$ from the curve $y=|x-1|+|x+1|$ is

• A. 1
• B. 0
• C. $\sqrt{2}$
• D. $\sqrt{\frac{3}{2}}$

Answer 1

The correct option is A

1

As show in the figure, we have
$y=\{\begin{array}{ccc}2x& \forall & x\ge 1\\ 2x& \forall & -1\le x<1\\ -2x& \forall & x<-1\end{array}$
The minimum distance / shortest distance is 2-1=1