Function f(x)= -2 is monotonic decreasing when:

MCQ

Function $\text{f}(\text{x})=\cos\text{x}-2\lambda\text{x}$ is monotonic decreasing when:

A
$\lambda>\frac{1}{2}$
B
$\lambda<\frac{1}{2}$
✓
$\lambda<2$
D
$\lambda>2$

✓

Answer

Correct option: C.

$\lambda<2$

$\text{f}(\text{x})=\cos\text{x}-2\lambda\text{x}$
$\text{f}'(\text{x})=-\sin\text{x}-2\lambda$
For f(x) to be decreasing, we must have
$\text{f}'(\text{x})<0$
$\Rightarrow-\sin\text{x}-2\lambda<0$
$\Rightarrow\sin\text{x}+2\lambda>0$
$\Rightarrow2\lambda>-\sin\text{x}$
We know that the maximum value of $-\sin\text{x}$ is 1.
$\Rightarrow2\lambda>1$
$\Rightarrow\lambda>\frac{1}{2}$

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 Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

${d \over {dx}}{({x^2} + \cos x)^4} = $

→

The probabilities of a student getting I, II and III division in an examination are $\frac{1}{10},\frac{3}{5}$ and $\frac{1}{4}$ respectively. The probability that the student fails in the examination is.

→

The function which is continuous for all real values of $x$ and differentiable at $x = 0$ is

→

If $y = {\sqrt x ^{{{\sqrt x }^{\sqrt x ....\infty }}}}$, then ${{dy} \over {dx}} = $

→

The area of the region between the curves $y=\sqrt{\frac{1+\sin x}{\cos x}}$ and $y=\sqrt{\frac{1-\sin x}{\cos x}}$ bounded by the lines $x=0$ and $x=\frac{\pi}{4}$ is

→

Let $a ,b ,c $ be such that $b + c \ne 0$ if

$\left| {\begin{array}{*{20}{c}}a&{a + 1}&{a - 1}\\{ - b}&{b + 1}&{b - 1}\\c&{c - 1}&{c + 1}\end{array}} \right| + \left| {\begin{array}{*{20}{c}}{a + 1}&{b + 1}&{c - 1}\\{a - 1}&{b - 1}&{c + 1}\\{{{\left( { - 1} \right)}^{n + 2}} \cdot a}&{{{\left( { - 1} \right)}^{n + 1}} \cdot b}&{{{\left( { - 1} \right)}^n} \cdot c}\end{array}} \right| = 0$ then $n$ equals to

→

Let $\text{f(x)}=\text{x}+\text{b}|\text{x}|+\text{c}|\text{x}|^4,$ where a, b, and c are real constants. Then, f (x) is differentiable at x = 0, if:

→

The values of $\mathrm{m}, \mathrm{n}$, for which the system of equations

$ x+y+z=4 $

$ 2 x+5 y+5 z=17 $

$ x+2 y+m z=n$

has infinitely many solutions, satisfy the equation :

→

Let the matrix $A$ and $B$ be defined as $A\, = \,\left[ {\begin{array}{*{20}{c}}
3&2 \\
2&1
\end{array}} \right]$ and $B\, = \,\left[ {\begin{array}{*{20}{c}}
3&1 \\
7&3
\end{array}} \right]$ , then the value of $det. \,(2A^9B^{-1}),$ is :-

→

Choose the correct answer from the given four options.
The value of $\sin\big[2\tan^{-1}(0.75)\big]$ is equal to: