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Let $f(x)=\left\{\begin{array}{ll}-2, & -3 \leq x \leq 0 \\ x-2, & 0 < x \leq 3\end{array}\right.$ and $g(x)=f(|x|)+|f(x)|$
What is the value of the differential coefficient of $g(x)$ at $x=-2$ ?
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What is the value of the differential coefficient of $g(x)$ at $x=-2$ ?
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For $x=-2$ $g(x)=-2+|-2|=-2+2$
$\Rightarrow g(x)=0$
$\Rightarrow$ differential coefficient at $x=-2$ is given as :
$g^{\prime}(x)=\lim _{h \rightarrow 0} \frac{g(x+h)-g(x)}{h}=\lim _{h \rightarrow 0} \frac{0-0}{4}=0 .$
$\Rightarrow g(x)=0$
$\Rightarrow$ differential coefficient at $x=-2$ is given as :
$g^{\prime}(x)=\lim _{h \rightarrow 0} \frac{g(x+h)-g(x)}{h}=\lim _{h \rightarrow 0} \frac{0-0}{4}=0 .$
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