Download App

STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
The function defined by $f(x) = \left\{ \begin{array}{l}|x - 3|\,;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \ge 1\\\frac{1}{4}{x^2} - \frac{3}{2}x + \frac{{13}}{4};\,x < 1\end{array} \right.$ is
  • A
    Continuous at $x = 1$
  • B
    Continuous at $x = 3$
  • C
    Differentiable at $x = 1$
  • ✓
    All the above
✓

Answer

Correct option: D.
All the above
d
(d) Since $|x - 3|\, = x - 3,$ if $x \ge 3$$ = - x + 3,$ if $x < 3$

$\therefore $ The given function can be defined as

$f(x) = \left\{ {\begin{array}{*{20}{r}}{\frac{1}{4}{x^2} - \frac{3}{2}x + \frac{{13}}{4},}&{x < 1\,\,\,\,\,\,\,\,}\\{3 - x,}&{1 \le x < 3}\\{x - 3,}&{x \ge 3\,\,\,\,\,\,\,}\end{array}} \right.$

Now proceed to check the continuity and differentiability at $x = 1.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $A=\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right]$, then adj $A$ is equal to
→
Construct a $3 \times 4$ matrix, whose elements are given by $a_{i j}=2 i-j$.
→
$\int_{}^{} {\frac{1}{{{x^2}{{({x^4} + 1)}^{3/4}}}}dx = } $
→
If A is a skew symmetric matrix, then ∣A∣ is
→
$\int|\text{x}|\text{dx}$ is equal to:
→
If $A = \left| {\,\begin{array}{*{20}{c}}{\sin (\theta + \alpha )}&{\cos (\theta + \alpha )}&1\\{\sin (\theta + \beta )}&{\cos (\theta + \beta )}&1\\{\sin (\theta + \gamma )}&{\cos (\theta + \gamma )}&1\end{array}\,} \right|$ ,then
→
$\int\frac{\text{x}^3}{\text{x}+1}\text{ dx}$ is equal to:
→
The coordinates of the point on the ellipse $16x^2+ 9y^2= 400$ where the ordinate decreases at the same rate at which the abscissa increases, are :
→
The differential equation for $\text{y}=\text{A}\cos\text{ax}+\text{B}\sin\text{ax}$ where $A$ and $B$ are arbitary constants is:
→
If $A=\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1\end{array}\right]$, then $(A-I)(A+I)=O$ for
→