Download App

STD 12 - 6. Application of derivatives — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 6. Application of derivatives4 Marks
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

If $\mathrm{A}(3,1,-1), \mathrm{B}\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right), \mathrm{C}(2,2,1)$ and $\mathrm{D}\left(\frac{10}{3}, \frac{2}{3}, \frac{-1}{3}\right)$ are the vertices of a quadrilateral $\mathrm{ABCD}$, then its area is
→
The value of the integral $\int_{-1}^2 \log _e\left(x+\sqrt{x^2+1}\right) d x$ is:
→
If the point $(a, 2a)$ falls between the lines $\left| {x + y + 1} \right| = 4$ then complete set of values of $'a'$ is
→
Let $A_1, A_2$ and $A_3$ be the regions on $R^2$ defined by

$A_1=\left\{(x, y): x \geq 0, y \geq 0,2 x+2 y-x^2-y^2>1>x+y\right\}$

$A_2=\left\{(x, y): x \geq 0, y \geq 0, x+y>1>x^2+y^2\right\}$

$A_3=\left\{(x, y): x \geq 0, y \geq 0, x+y>1>x^3+y^3\right\}$

Denote by $\left|A_1\right|,\left|A_2\right|$ and $\left|A_3\right|$ the areas of the regions $A_1, A_2$ and $A_3$ respectively. Then,

→
$\int_{}^{} {\frac{{\sqrt {{x^2} + 1} [\log ({x^2} + 1) - 2\log x]}}{{{x^4}}}} dx$ is equal to
→
The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is
→
Let for $x \in R , S_0( x )= x$,$S _{ k }( x )= C _{ k } x + k \int _0^{ x } S _{ k -1}(t) d t$, where $C _0=1, C _{ k }=1-\int_0^1 S _{ k -1}( x ) dx , k =1,2,3 \ldots$. Then $S _2(3)+6 C _3$ is equal to $...........$.
→
Given equation $4x^2 + 4(a -1)x + (1 -2a) = 0$ has roots $sin\,\theta$ and $cos\,\theta\,(0<\theta<\frac{\pi}{2})$, then maximum value of $(a + sin\,\theta)$ is-
→
Let $2^{\text {nd }}, 8^{\text {th }}$ and $44^{\text {th }}$, terms of a non-constant $A.P.$ be respectively the $1^{\text {st }}, 2^{\text {nd }}$ and $3^{\text {rd }}$ terms of $G.P.$ If the first term of $A.P.$ is $1$ then the sum of first $20$ terms is equal to-
→
If $f:R \to R$, then $f(x) = \;|x|$ is
→