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
Let $f:R \to R$ be a function defined by $f(x) = \max \,(x,\,{x^3}).$ The set of all points where $f(x)$ is not differentiable is
  • A
    $\{ - 1,\,1\} $
  • B
    $\{ - 1,\,\,0\} $
  • C
    $\{ 0,\,\,1\} $
  • ✓
    $\{ - 1,\,\,0,\,1\} $
✓

Answer

Correct option: D.
$\{ - 1,\,\,0,\,1\} $
d
(d) If $x < - 1$ then $x > {x^3}$. So, $f(x) = x$,
If $x = - 1$ then $x = {x^3}$. So, $f(x) = x$,
If $ - 1 < x < 0$ then $x < {x^3}$. So, $f(x) = {x^3}$,
If $x = 0$ then $x = {x^3}$. So, $f(x) = {x^3}$,
If $0 < x < 1$ then $x > {x^3}$. So, $f(x) = x$,
If $x = 1$ then $x = {x^3}$. So, $f(x) = x$,
If $x > 1,$ then $x < {x^3}$. So, $f(x) = {x^3}$
Thus $f(x) = x,\,x \le - 1$,$f(x) = \left\{ {\begin{array}{*{20}{c}}x&,&{x \le - 1}\\{{x^3}}&,&{ - 1 < x \le 0}\\x&,&{0 < x \le 1}\\{{x^3}}&,&{x > 1}\end{array}} \right.$
Clearly, $f(x)$ is not differentiable at $x = - 1,\,0,\,1$.

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

The equation of the plane through point $(1, 2, -3)$ which is parallel to the plane $3x - 5y + 2z = 11$ is given by:
→
The area bounded by $y - 1 = |x|, y = 0$ and $|x| =\frac{1}{2}$ will be:
→
The order of the differential equartion $\sqrt{1-\text{x}^{4}}+\sqrt{1-\text{y}^{4}}=\text{a}(\text{x}^{2}-\text{y}^{2})$ is:
→
Simplify $ {\cot ^{ - 1}}\frac{1}{{\sqrt {{\text{x}^2} - 1} }}$ for $\text{ x} < - 1$:
→
A continuously differentiable function $\phi (x)\,{\rm{in}}\,(0,\,\pi )$ satisfying $y' = 1 + {y^2},\,\,y(0) = 0 = y(\pi )$ is
→
The area of the region bounded by the parabola $y=\sin ^2 x$, lines $x=\frac{\pi}{2}, x=\pi$ and $x$-axis is :
→
The sum of the maximum and minimum values of the function $f(x)=|5 x-7|+\left[x^{2}+2 x\right]$ is the interval $\left[\frac{5}{4}, 2\right]$, where $[ t ]$ is the greatest integer $\leq t$ is $.......$
→
$\int\sqrt{\frac{\text{x}}{1-\text{x}}}\text{ dx}$ is equal to:
→
$y = ke^{\sin ^{-1} x} + 3$ is a solution of differeulial equation :-
→
Evaluate: $\int \frac{\sin x}{1+\sin x} d x$
→