Q68 / 170 · Manipal (MET) 2019 · Mathematics

The derivative of $f(x)=3|2+x|$ at the point $x_0=-3$ is

  • A
    $3$
  • Correct answer
    B
    $-3$
  • C
    $0$
  • D
    None of the above

Solution

We have, $f(x)=3|2+x|$ as $f(x)=|x| \Rightarrow f^{\prime}(x)=\frac{x}{|x|}$ Now, $f(x)=3|x+2|$ $\Rightarrow \quad f(x)=3 \frac{x+2}{|x+2|}=-3 \quad\left(\right.$ as $\left.x_0=-3\right)$

Hence, the correct answer is option: 'B'.

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