The function f(x) = x + x has - Vidyadip

MCQ

The function $f(x) = x + \sin x$ has

A
A minimum but no maximum
B
A maximum but no minimum
✓
Neither maximum nor minimum
D
Both maximum and minimum

✓

Answer

Correct option: C.

Neither maximum nor minimum

c
(c) $ f(x) = x + \sin x$ ==> $f'(x) = 1 + \cos x$

Now $f'(x) = 0 \Rightarrow 1 + \cos x = 0 \Rightarrow \cos x = - 1 \Rightarrow x = \pi $

Now $f''(x) = - \sin x$,$f''(\pi ) = 0$,,

$f'''(\pi ) = 1 \ne 0$

$\therefore$ Neither maximum nor minimum.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of first four observations is $\frac{7}{2}$, then the variance of the first four observations in equal to

The equation of the locus of all points equidistant from the point $(4,2)$ and the $x$-axis, is

One vertex of the equilateral triangle with centroid at the origin and one side as $x + y - 2 = 0$ is

The expression,$\frac{{\tan \,\left( {{\textstyle{{3\,\pi } \over 2}}\,\, - \,\,\alpha } \right)\,\,\,\cos \,\left( {{\textstyle{{3\,\pi } \over 2}}\,\, - \,\,\alpha } \right)}}{{\cos \,(2\,\pi \,\, - \,\alpha )}}$ $+ cos \left( {\alpha \,\, - \,\,\frac{\pi }{2}} \right) \,sin (\pi -\alpha ) + cos (\pi +\alpha ) sin \,\left( {\alpha \,\, - \,\,\frac{\pi }{2}} \right)$ when simplified reduces to :

Let $e_{1}$ and $e_{2}$ be the eccentricities of the ellipse $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{25}=1$ and the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{b^{2}}=1$, respectively. If $\mathrm{b}<5$ and $\mathrm{e}_{1} \mathrm{e}_{2}=1$, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is :

A contest consists of predicting the results win, draw or defeat of $7$ football matches. $A$ sent his entry by predicting at random. The probability that his entry will contain exactly $4$ correct predictions is

A biased die is tossed and the respective probabilities for various faces to turn up are given below

$Face:$	$1$	$2$	$3$	$4$	$5$	$6$
$P(F)$	$0.1$	$0.24$	$0.19$	$0.18$	$0.15$	$0.14$

If an even face has turned up, then the probability that it is face $2$ or face $4$, is

The equation of a circle is $\operatorname{Re}\left(z^{2}\right)+2(\operatorname{Im}(z))^{2}+2 \operatorname{Re}(z)=0$, where $z=x+$ iy. A line which passes through the center of the given circle and the vertex of the parabola, $x^{2}-6 x-y+13=0,$ has $y$-intercept equal to $.....$

Let $P=\{\theta: \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and $Q=\{\theta: \sin \theta+\cos \theta=\sqrt{2} \sin \theta\}$ be two sets. Then

The number of real values $\lambda$, such that the system of linear equations $2 x-3 y+5 z=9$ ; $x+3 y-z=-18$ ; $3 x-y+\left(\lambda^{2}-1 \lambda \mid\right) z=16$ has no solution, is :-