Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
The function $f(x)=\left\{\begin{array}{cc}|x-3|, & x \geq 1 \\ \frac{x^2}{4}-\frac{3 x}{2}+\frac{13}{4}, & x<1\end{array}\right.$ is
  • A
    continuous at $x=1$
  • B
    differentiable at $x=1$
  • C
    continuous at $x=3$
  • ✓
    All of these
✓

Answer

Correct option: D.
All of these
$ |x-3|$ is continuous at $x=3$, but not differentiable.
$f\left(1^{-}\right)=f\left(1^{+}\right)=f(1)=2$
$f^{\prime}\left(1^{-}\right)=f^{\prime}\left(1^{+}\right)=-1=f^{\prime}(1)$
$\therefore f(x)$ is continuous and differentiable 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 Continuity and Differentiability→Continuity and Differentiability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

He area of the region bounded by the parabola $y = x^2$ and $y = |x|$ is:
→
$\mathop {\lim }\limits_{n \to \infty } \frac{1}{{{1^3} + {n^3}}} + \frac{4}{{{2^3} + {n^3}}} + .... + \frac{1}{{2n}}$ is equal to
→
The point$(s),$ at which the function $f$ given by $f(x)=\left\{\begin{array}{l}\frac{x}{|x|}, x<0 \\ -1, x \geq 0\end{array}\right.$ is continuous, is$/$are
→
$\int\frac{\text{dx}}{\sqrt{\text{x}}}=$
→
The curve $y-x:$
→
Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is
→
Let $f$ be a differentiable function satisfying the relation $f(xy) = xf(y) + yf(x) -2xy$ (where $x,y > 0)$ and $f'(1) = 3$, then 
→
Choose the correct answer:$\text{Let}\ \vec{\text{a}}\ \text{and}\ \vec{\text{b}}$ be two unit vectors and $\theta$ is the angle between them. Then $\vec{\text{a}}+\vec{\text{b}}$ is a unit vector if,
→
Let $\vec{a}=4 \hat{i}+3 \hat{j}$ and $\vec{b}=3 \hat{i}-4 \hat{j}+5 \hat{k}$ and $\vec{c}$ is a vector such that $\overrightarrow{ c } \cdot(\overrightarrow{ a } \times \overrightarrow{ b })+25=0, \overrightarrow{ c } \cdot(\hat{ i }+\hat{ j }+\hat{ k })=4$ and projection of $\overrightarrow{ c }$ on $\overrightarrow{ a }$ is $1,$ then the projection of $\overrightarrow{ c }$ on $\overrightarrow{ b }$ equals:
→
Let a function $h(x)$ be defined as $h(x) = 0$, for all $x \ne 0$. Also $\int\limits_{ - \,\infty }^\infty  {{\rm{h}}(x)\,\cdot\,{\rm{f}}(x)\,dx} $ $= f (0)$, for every function $f (x)$. Then the value of the definite integral $\int\limits_{ - \,\infty }^\infty  {{\rm{h}}'(x)\,\cdot\,\sin x\,dx} $, is
→