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  4. The value of the derivative of |x - 1| + | x - 3 | at x = 2 is

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Q. The value of the derivative of $|x - 1| + | x - 3 | $at $x = 2$ is

Limits and Derivatives

Solution:

Given : $f(x) = |x - 1 | + | x -3 |$
At $x = 2, |x - 1| = x - 1$
and $| x -3 | = - x + 3$
$\Rightarrow f(x) = x - 1 - x + 3= 2$
which is a constant function
$\Rightarrow f'(2) = 0$