Question

What is the derivative of $|x-1|$ at $x=2$?

• A. $-1$
• B. $0$
• C. $1$
• D. Derivative does not exist

Answer 1

Answer: (C)

$1$

given $f\left(x\right)=|x-1|$

$f\left(x\right)=(x-1)$ when $x-1>0$ i.e. $x>1$

$f\left(x\right)=-(x-1)=1-x$ when $x-1<0$ i.e. $x<1$

So, at $x=2,f\left(x\right)=x-1$

$\frac{df}{dx}=1$

Thus, derivative of $f$ at $x=2$ is $1$.