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Question
Write the derivative of f (x) = 3 |2 + x| at x = −3.
Solution
\[\text{ Let } x = -3\]
\[\text{ We know }:\]
\[-3<-2\]
\[\text{ Thus, we have }:\]
\[x<-2\]
\[\text{ It gives } x+2<0.\]
\[ \therefore \left| 2 + x \right| = \left| x + 2 \right| = - \left( x + 2 \right) = - x - 2\]
\[f\left( x \right) = 3 \left| 2 + x \right| = 3\left( - x - 2 \right) = - 3x - 6\]
\[f'\left( x \right) = - 3\frac{d}{dx}\left( x \right) - \frac{d}{dx}\left( 6 \right) = - 3\]
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