Given [0,20], then number of integral values of for which the fun… - Vidyadip

MCQ

Given $\lambda \in [0,20]$, then number of integral values of $\lambda$ for which the function $f(x) = x^3 -12x + \lambda$ has a point of maxima-

A
$5$
B
$4$
C
$0$
✓
$21$

✓

Answer

Correct option: D.

$21$

d
$\because f(\mathrm{x})=\mathrm{x}^{3}-12 \mathrm{x}+\lambda \Rightarrow f^{\prime}(\mathrm{x})=3(\mathrm{x}-2)(\mathrm{x}+2)$

clearly $f(\mathrm{x})$ is maximum at $\mathrm{x}=-2 \forall \lambda \in[0,20]$

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

If $\int {\frac{{(2{x^2} + 1)\,\,dx}}{{({x^2} - 4)\,\,({x^2} - 1)}} = \log \left[ {{{\left( {\frac{{x + 1}}{{x - 1}}} \right)}^a}\,\,{{\left( {\frac{{x - 2}}{{x + 2}}} \right)}^b}} \right]} + C,$ then the values of $a$ and $b$ are respectively

The area, enclosed by the curves $y=\sin x+\cos x$ and $\mathrm{y}=|\cos \mathrm{x}-\sin \mathrm{x}|$ and the lines $\mathrm{x}=0, \mathrm{x}=\frac{\pi}{2}$ is:

If $A =\left[\begin{array}{cc}\cos x & \sin x \\ -\sin x & \cos x\end{array}\right]$ and $A (\operatorname{adj} A )= KI$ then value of $K$ will be :

Tho damnin of tho finction $\cos ^{-1}\left(\frac{2 \sin ^{-1}\left(\frac{1}{4 x^{2}-1}\right)}{\pi}\right)$ is

Choose the correct answer from the given four options.The plane $2x – 3y + 6z – 11 = 0$ makes an angle $\sin^{-1}(\alpha)$ with $x-$axis. The value of $\alpha$ is equal to:

The area(in sq. units) of the region bounded by the curves $y = 2^x$ and $y = |x +1|$ in the first quadrant is

Let for a triangle $ABC$,

$\overline{A B}=-2 \hat{i}+\hat{j}+3 \hat{k}$

$\overline{C B}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$

$\overline{C A}=4 \hat{i}+3 \hat{j}+\delta \hat{k}$

If $\delta > 0$ and the area of the triangle $ABC$ is $5 \sqrt{6}$, then $\overline{C B} \cdot \overline{C A}$ is equal to

Choose the correct answer from the given four options: Area of the region in the first quadrant enclosed by the $x-$axis, the line $y = x$ and the circle $x^2 + y^2 = 32$ is:

If the function $f : R \rightarrow R$ be such that $f(x) = x - [x]$, where [x] denotes the greatest integer less than or equal to $x,$ then $f^{-1}(x)$ is:

Value of $\int\frac{\text{dx}}{\sqrt{2\text{x}-\text{x}^2}}$