Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives1 Mark
Question
If f(x) = |x| + |x - 1|, write the value of $\frac{\text{d}}{\text{dx}}\big(\text{f}(\text{x})\big)$
✓
Answer
$\text{f}(\text{x})=|\text{x}|+|\text{x}+1|$When x > 1
$\text{f}(\text{x})=\text{x}+\text{x}-1=\text{2x}-1$
$\frac{\text{d}}{\text{dx}}\big(\text{f}(\text{x})\big)=2$
When 0 < x < 1
$\text{f}(\text{x})=\text{x}-\text{x}+1=1$
$\frac{\text{d}}{\text{dx}}\big(\text{f}(\text{x})\big)=0$
When x < 0
$\text{f}(\text{x})=-\text{x}-\text{x}+1=-\text{2x}+1$
$\frac{\text{d}}{\text{dx}}\big(\text{f}(\text{x})\big)=-2$
$\frac{\text{d}}{\text{dx}}\big(\text{f}(\text{x})\big)=\begin{cases}2,&\text{x}>1\\0,&0<\text{x}<1\\-2,&\text{x}<0\end{cases}$
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