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Question
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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Solution
\[\text{ Let } x = 2\]
\[\text{ We know }:\]
\[2>1 \text{ and } 2<3\]
\[\therefore x>1 \text{ and } x<3\]
\[\left| x - 1 \right| = x - 1 \text{ and } \left| x - 3 \right| = - \left( x - 3 \right) = - x + 3\]
\[f\left( x \right) = \left| x - 1 \right| + \left| x - 3 \right| = x - 1 - x + 3 = 2\]
\[f'\left( x \right) = 0\]
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