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Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation2 Marks
MCQ
The function $r(x)=\left\{\begin{array}{cc}|x-3|, & x \geq 1 \\ \frac{x^2}{4}-\frac{3 x}{2}+\frac{13}{4}, & x<1\end{array}\right.$ is
  • A
    continuous at $x=1$
  • ✓
    differentiable at $x=1$
  • C
    continuous at $x=3$
  • D
    All of these
✓

Answer

Correct option: B.
differentiable at $x=1$
$(d) : |x-3|$ is continuous at $x=3$, but not differentiable.
$f\left(1^{-}\right)=f\left(1^{+}\right)=f(1)=2$
$f^{\prime}\left(1^{-}\right)=f\left(1^{+}\right)=-1=f(1)$
$\therefore f(x)$ is continuous and differentiable at $x=1$.

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