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Substitution Method to Remove Indeterminate Form

Write the der...

Question

Write the derivative of $f (x) = 3 | 2 + x | at x = - 3$ .

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Solution

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$f (x) = 3 | 2 + x |$

$f (x) = {\begin{matrix} 3 (2 + x) & a t x > - 2 - 3 (2 + x) & a t x < - 2 \end{matrix}}$

$Since x = - 3, therefore f (x) = - 3 (2 + x)$

$f^{'} (x) = - 3$

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