# Write the Value of the Derivative of F (X) = |X − 1| + |X − 3| at X = 2. - Mathematics

Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.

#### Solution

$\text{ Let } x = 2$
$\text{ We know }:$
$2>1 \text{ and } 2<3$
$\therefore x>1 \text{ and } x<3$
$\left| x - 1 \right| = x - 1 \text{ and } \left| x - 3 \right| = - \left( x - 3 \right) = - x + 3$
$f\left( x \right) = \left| x - 1 \right| + \left| x - 3 \right| = x - 1 - x + 3 = 2$
$f'\left( x \right) = 0$

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 8 | Page 47