Let f(x) = l ( 3 - , ( 1/x ) ) , | x |, , , , ,x 0 0, , , , , , ,… - Vidyadip

MCQ

Let $f(x) = \left\{ \begin{array}{l}
\left( {3 - \sin \,\left( {1/x} \right)} \right)\,\left| x \right|,\,\,\,\,x \ne 0\\
0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0\,\,
\end{array} \right.\,$ . Then at $x = 0 , f$ has a

A
maxima
✓
minima
C
Neither maxima nor minima
D
Point of discontinuity

✓

Answer

Correct option: B.

minima

b
$f$ is continous at $\mathrm{x}=0$

Further $f(0+h)>f(0)$ and $f(0-h)>f(0),$ for positive $'h'.$

Hence $f$ has minimum value at $x=0$.

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 - 6. Application of derivatives→STD 12 - 6. Application of derivatives — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Write the number of points where $f(x) = |x + 2| + |x - 3|$ is not differentiable :

$\int\limits_0^{4\,/\,\pi } {} $ $\left( {3\,{x^2}\,\,.\,\,\sin \,\frac{1}{x}\,\, - \,\,x\,\,.\,\,\cos \,\frac{1}{x}} \right)$ $dx$ has the value :

Degree of the given differential equation ${\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^3} = {\left( {1 + \frac{{dy}}{{dx}}} \right)^{1/2}}$, is

Which one of the following is not bounded on the intervals as indicated

If x < 0, y < 0 such that xy = 1, then $\tan^{-1}\text{x}+\tan^{-1}\text{y}$ equals:

If $a+x=b+y=c+z+1,$ where $a, b, c, x, y, z$ are non-zero distinct real numbers, then $\left|\begin{array}{lll}x & a+y & x+a \\ y & b+y & y+b \\ z & c+y & z+c\end{array}\right|$ is equal to

If $f : R \rightarrow R$ is given by $f(x) = 3x - 5,$ then $f^{-1}(x)$

A bag ‘$A$’ contains $2$ white and $3$ red balls and bag ‘$B$’ contains $4$ white and $5$ red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag $‘B’$ was

If $\left[ {\begin{array}{*{20}{c}}
2&1 \\
1&2
\end{array}} \right]$ $A\left[ {\begin{array}{*{20}{c}}
{ - 3}&2 \\
5&{ - 3}
\end{array}} \right] = {I_2}$ then $A =$

Let $A$ be a non-zero periodic matrix with period $4$ and $A^{12} + B =I$, where $I$ is identity matrix and $B$ is any square matrix of same order as of $A$. Matrix product $AB$ is equal to