A) Continuous at \[x=1\]
B) Continuous at \[x=3\]
C) Differentiable at \[x=1\]
D) All the above
Correct Answer: D
Solution :
Since \[|x-3|\,=x-3,\] if \[x\ge 3\]\[=-x+3,\] if \[x<3\] \[\therefore \] The given function can be defined as \[f(x)=\left\{ \begin{array}{*{35}{r}} \frac{1}{4}{{x}^{2}}-\frac{3}{2}x+\frac{13}{4}, & x<1\,\,\,\,\,\,\,\, \\ 3-x, & 1\le x<3 \\ x-3, & x\ge 3\,\,\,\,\,\,\, \\ \end{array} \right.\] Now proceed to check the continuity and differentiability at \[x=1.\]
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