MCQ
$f(x) = \left| {\left| x \right| - 1} \right|$ is not differentiable at
- A$0$
- ✓$ \pm 1,\,0$
- C$1$
- D$ \pm \,1$
✓
Answer
Correct option: B.
$ \pm 1,\,0$
b
(b )$ = \left\{ \begin{array}{l}|x| - 1,\,\,\,\,\,\,\,|x| - 1 \ge 0\\ - |x| + 1,\,\,\,|x| - 1 < 0\end{array} \right.$
(b )$ = \left\{ \begin{array}{l}|x| - 1,\,\,\,\,\,\,\,|x| - 1 \ge 0\\ - |x| + 1,\,\,\,|x| - 1 < 0\end{array} \right.$
$ = \left\{ \begin{array}{l}|x| - 1,\,\,\,x \le - 1\,\,{\rm{or}}\,x \ge 1\\ - |x| + 1,\,\,\,\,\,\,\, - 1 < x < 1\end{array} \right.$
$ = \left\{ \begin{array}{l} - x - 1,\,\,\,\,\,x \le - 1\\x + 1,\,\,\,\,\,\, - 1 < x < 0\\ - x + 1,\,\,\,\,\,0 \le x < 1\\\,\,x - 1,\,\,\,\,\,\,\,x \ge 1\end{array} \right.$
From the graph. It is clear that $f(x)$ is not differentiable at $x = - 1,\,0$ and $1$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Differential coefficient of $\sec(\tan^{-1}\text{x})$ is:
→- $\frac{\text{x}}{1+\text{x}^2}$
- $\text{x}\sqrt{1+\text{x}^2}$
- $\frac{\text{x}}{\sqrt{1+\text{x}^2}}$
- $\frac{\text{x}}{\sqrt{1+\text{x}^2}}$
If $\vec{\text{a}}$ and $\vec{\text{b}}$ be two unit vectors and $\theta$ the angle between them, than $\vec{\text{a}}+\vec{\text{b}}$ is a unit vector if $\theta=$
→- $\frac{\pi}{4}$
- $\frac{\pi}{3}$
- $\frac{\pi}{2}$
- $\frac{2\pi}{3}$
$\int_{ - \pi /2}^{\pi /2} {\frac{{\cos x}}{{1 + {e^x}}}\,dx = } $
→If $2xy^3dx + x^2y^2dy = ydx -xdy$ and $y(2) =1$, then value of $y(-1)$ will be (where $y(x)$ denotes value of $y$ for given $x$) -
→$\int_{}^{} {(1 + 2x + 3{x^2} + 4{x^3} + ......)\;dx = } $
→Let $\mathrm{f}$ be a real-valued function defined on the interval $(-1,1)$ such that $e^{-x} f(x)=2+\int_0^x \sqrt{t^4+1} d t$, for all $\mathrm{x}$ $\in(-1,1)$ and let $f^{-1}$ be the inverse function of $f$. Then $\left(f^1\right)^{\prime}(2)$ is equal to
→If the distance travelled by a point in time $ t $ is $s = 180t - 16{t^2}$, then the rate of change in velocity is ......... $unit$
→The value of the integral $\int\limits^{\frac{\pi}{2}}_0\frac{\sqrt{\cos\text{x}}}{\sqrt{\cos\text{x}}+\sqrt{\sin\text{x}}}\text{ dx}$ is:
→- $0$
- $\frac{\pi}{2}$
- $\frac{\pi}{4}$
- none of these.
Least value of $\frac{{{x^2}{y^2} - 2{x^2}y + 2{x^2} + 2xy - 2x + 1}}{{{x^2}y + x}}$ is $\lambda $, then
→{where $x,y \in R^+, x^2y + x \ne 0$ }
The corner points of the shaded unbounded feasible region of an LPP are $(0,4),(0.6,1.6)$ and $(3,0)$ as shown in the figure. The minimum value of the objective function $Z=4 x+6 y$ occurs at
→