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

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

Similar questions

Which one of the following statement is True ?

The sum of first $n$ terms of the given series ${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + ............$ is $\frac{{n{{(n + 1)}^2}}}{2}$, when $n$ is even. When $n$ is odd, the sum will be

Let $g (x)$ be an antiderivative for $f (x)$. Then $ln \,\left( {1 + {{\left( {g(x)} \right)}^2}} \right)$ is an antiderivative for

The general solution of ${x^2}\frac{{dy}}{{dx}} = 2$ is

The locus of $z$ satisfying the inequality ${\log _{1/3}}|z + 1|\, > $ ${\log _{1/3}}|z - 1|$ is

$\int\limits_{ - 3\pi }^{3\pi } {{{\sin }^2}\,\theta {\mkern 1mu} si{n^2}\,2\,\theta d\theta } $ is equal to

$\frac{{\frac{1}{2}.\frac{2}{2}}}{{{1^3}}} + \frac{{\frac{2}{2}.\frac{3}{2}}}{{{1^3} + {2^3}}} + \frac{{\frac{3}{2}.\frac{4}{2}}}{{{1^3} + {2^3} + {3^3}}} + .....n$ terms =

Let $a_{1}, a_{2}, \ldots, a_{10}$ be an $AP$ with common difference $-3$ and $\mathrm{b}_{1}, \mathrm{~b}_{2}, \ldots, \mathrm{b}_{10}$ be a $GP$ with common ratio $2.$ Let $c_{k}=a_{k}+b_{k}, k=1,2, \ldots, 10 .$ If $c_{2}=12$ and $\mathrm{c}_{3}=13$, then $\sum_{\mathrm{k}=1}^{10} \mathrm{c}_{\mathrm{k}}$ is equal to ..... .

Maximum area of a circle centered at origin, which is inscribed in the parabola $y = x^2 - 100$, can be expresed as $\frac{{a\pi }}{b}$,where $a$ and $b$ are coprime numbers, then the value of $a + b$ is

The lines $\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{L}_{20}$ are distinct. For $\mathrm{n}=1,2,3, \ldots, 10$ all the lines $\mathrm{L}_{2 \mathrm{n}-1}$ are parallel to each other and all the lines $L_{2 n}$ pass through a given point $P$. The maximum number of points of intersection of pairs of lines from the set $\left\{\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{L}_{20}\right\}$ is equal to :