Question

If $f\left(x\right)=\left|x-2\right|+\left|x+1\right|-x$, then $f\text{'}\left(-10\right)$ is equal to

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

Answer 1

The correct option is A

$-3$

Explanation for the correct option:

Finding the value of the expression:

Given that,

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

Differentiate the given function with respect to $x$.

$f\text{'}\left(x\right)=\frac{\left|x-2\right|}{x-2}+\frac{\left|x+1\right|}{x+1}-1\left[\because \frac{d\left|x\right|}{dx}=\frac{\left|x\right|}{x}or\frac{x}{\left|x\right|}\right]$

Now, substitute $x=-10$ in the derivative,

$\begin{array}{rcl}f\text{'}\left(-10\right)& =& \frac{\left|-10-2\right|}{-10-2}+\frac{\left|-10+1\right|}{-10+1}-1\\ & =& \frac{12}{-12}+\left(\frac{9}{-9}\right)-1\\ & =& -3\end{array}$

Hence, the correct option is A.