Let f ( x ), x [ 0, ) be a non-negative continuous function. If f… - Vidyadip

MCQ

Let $f\left( x \right), x \in \left[ {0,\infty } \right)$ be a non-negative continuous function. If $f'\left( x \right)\cos x \le f\left( x \right)\sin x\ \forall\, x \ge 0$, then the value of $f(2\pi)$ is equal to

✓
$0$
B
$1$
C
$\pi$
D
None of these

✓

Answer

Correct option: A.

$0$

a
$f^{\prime}(x) \cos x \leq f(x) \sin x$

$f^{\prime}(x) \cos x-f(x) \sin x \leq 0$

$(f(x) \cos x)^{\prime} \leq 0$

$\therefore $ $g(x)=f(x) \cos x$ is a monotonically nonincreasing function.

Since $\mathrm{f}(\mathrm{x})$ is non-negative, $\mathrm{f}(2 \pi)=0$

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

The probability distribution of a discrete random variable X is given below:

$\text{X}:$	$2$	$3$	$4$	$5$
$\text{P}(\text{X}):$	$\frac{5}{\text{k}}$	$\frac{7}{\text{k}}$	$\frac{9}{\text{k}}$	$\frac{11}{\text{k}}$

The value of k is:

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12\,A$ is equal to $...........$.

$\int\limits^{\frac{\pi}{3}}_{\frac{\pi}{6}}\frac{1}{1+\sqrt{\cot\text{x}}}\text{ dx}$ is:

For what value of $k$, the function given below is continuous at $x=0 \ ? f(x)=\left\{\begin{array}{cc}\frac{\sqrt{4+x}-2}{x} & , x \neq 0 \\ k & , x=0\end{array}\right.$

If X is a binomial variate with parameters n and p, where 0 < p < 1 such that $\frac{\text{P(X = r)}}{\text{P(X = n - r})}$ is independent of n and r, then p equals:

The value of $\int\limits_0^1 {\frac{{{x^4}{{(1 - x)}^4}}}{{1 + {x^2}}}dx} $ is equal to

The direction cosines $l, m, n$ of two lines are connected by the relations $l + m + n = 0, lm = 0,$ then the angle between them is:

If $\vec a = 3\vec j + 4\vec k$ , $\vec b = 2\vec i + \vec k$ and $\vec c$ , $\vec d$ are respectively the component of $\vec a$ parallel & perpendicular to $\vec b$ ,then $\left[ {\left( {\vec a \times \vec c} \right) \times \left( {\vec c \times \vec d} \right)\,\left( {\vec c \times \vec d} \right) \times \left( {\vec d \times \vec a} \right)\left( {\vec d \times \vec a} \right) \times \left( {\vec a \times \vec c} \right)} \right]$ equals

Choose the correct answer from the given four options : Let the $f : R \rightarrow R$ be defined by $\text{f(x)}=2\text{x}+\cos\text{x}$ then $f :$

Let $\quad f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{array}\right|$, $x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right]$. If $\alpha$ and $ \beta$ respectively are the maximum and the minimum values of $f$, then