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  4. The derivative of f(x)=3|2+x| at the point x0=-3 is

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Q. The derivative of $f(x)=3|2+x|$ at the point $x_{0}=-3$ is

ManipalManipal 2019

Solution:

We have, $f(x)=3|2+x|$
as $f(x)=|x| \Rightarrow f'(x)=\frac{x}{|x|}$
Now, $f(x)=3|x+2|$
$\Rightarrow f(x)=3 \frac{x+2}{|x+2|}=-3\left(\right.$ as $\left.x_{0}=-3\right)$