Function f(x) = 4 x^2 + 1 x is decreasing for interval - Vidyadip

MCQ

Function $f(x) = {{4{x^2} + 1} \over x}$ is decreasing for interval

A
$\left( {{{ - 1} \over 2},\,{1 \over 2}} \right)$
✓
$\left[ {{1 \over 2},\, - {1 \over 2}} \right]$
C
$(-1, 1)$
D
$[1, -1]$

✓

Answer

Correct option: B.

$\left[ {{1 \over 2},\, - {1 \over 2}} \right]$

b
(b) $f(x) = 4x + \frac{1}{x}$

$\frac{d}{{dx}}f(x) = \frac{d}{{dx}}\left[ {4x + \frac{1}{x}} \right] $

$= 4 - \frac{1}{{{x^2}}}$

For extremum, $\frac{{dy}}{{dx}} = 0$

==> $4 - \frac{1}{{{x^2}}} = 0$

==> $x = \frac{1}{2},\, - \frac{1}{2}$

$f\;\left( {\frac{1}{2}} \right) = 4.\frac{1}{2} + \frac{1}{{1/2}}$ = $2 + 2 = 4$

$f\;\left( { - \frac{1}{2}} \right) = 4.\left( { - \frac{1}{2}} \right) + \frac{1}{{ - 1/2}} = - 2 - 2 = - 4$

Hence $f(x)$ is decreasing in interval $[1/2,\, - 1/2]$.

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 6. Application of derivatives→6. Application of derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_{}^{} {{{\{ 1 + 2\tan x(\tan x + \sec x)\} }^{1/2}}dx = } $

In a sphere the rate of change of surface area is:

$8\pi$ times the rate of change of diameter.
$2\pi$ times the rate of change of diameter.
$2\pi$ times the rate of change of radius.
$8\pi$ times the rate of change of radius.

For any 2 × 2 matrix, if $\text{A(adj A)}=\begin{bmatrix} 10 & 0 \\ 0 & 10 \end{bmatrix},$ then |A| is equal to:

20
100
10
0

$\int_0^{\pi /2} {\frac{{x\sin x\cos x}}{{{{\cos }^4}x + {{\sin }^4}x}}} \,dx = $

Feasible region for an L.P.P. is shown shaded in the following figure. Minimum of $Z=5 x+3 y$ occurs at the point point

$\int\limits_0^{4\,/\,\pi } {} $ $\left( {3\,{x^2}\,\,.\,\,\sin \,\frac{1}{x}\,\, - \,\,x\,\,.\,\,\cos \,\frac{1}{x}} \right)$ $dx$ has the value :

If $\text{A}=\begin{vmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}\end{vmatrix}$ and C_ij is cofactor of a_ij in a, then value of |A| is given by:

a₁₁C₃₁ + a₁₂C₃₂ + a₁₃C₃₃
a₁₁C₁₁ + a₁₂C₂₁ + a₁₃C₃₁
a₂₁C₁₁ + a₂₂C₁₂ + a₂₃C₁₃
a₁₁C₁₁ + a₂₁C₂₁ + a₁₃C₃₁

The system of vectors i, j, k is:

Orthogonal
Collinear
Coplana
None of these

If the area bounded by $y = a{x^2}$ and $x = a{y^2}$, $a > 0$, is $1$, then $a = $

Let $f:R \to R,$ be a continuous function defined by $f\left( x \right) = \frac{1}{{{e^x} + 2{e^{ - x}}}}$

Statement $-1 :$ $f\left( c \right) = \frac{1}{3}$ for some $c\; \in R$

Statement $-2 :$$0 < f\left( x \right) < \frac{1}{{2\sqrt 2 }}\;,\forall x\; \in R$