The function f(x)=2 x+3(x)^ 2 3 , x R, has - Vidyadip

MCQ

The function $f(x)=2 x+3(x)^{\frac{2}{3}}, x \in R,$ has

A
exactly one point of local minima and no point of local maxima
B
exactly one point of local maxima and no point of local minima
C
exactly one point of local maxima and exactly one point of local minima
D
exactly two points of local maxima and exactly one point of local minima

✓

Answer

$f(x)=2 x+3(x)^{\frac{2}{3}}$
$f^{\prime}(x)=2+2 x^{\frac{-1}{3}}$
$=2\left(1+\frac{1}{x^{\frac{1}{3}}}\right)$
$=2\left(\frac{x^{\frac{1}{3}}+1}{x^{\frac{1}{3}}}\right)$

So, maxima $(M)$ at $x=-1 \ \operatorname{minima}(m)$ at $x=0$

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 $y = tan x \,\,tan 2x\,\, tan 3x$ then $\frac{{dy}}{{dx}}$ has the value equal to :

If $A, B, C$ be the angles of a triangle, then $\left| {\,\begin{array}{*{20}{c}}{ - 1}&{\cos C}&{\cos B}\\{\cos C}&{ - 1}&{\cos A}\\{\cos B}&{\cos A}&{ - 1}\end{array}\,} \right| = $

Solution of the equation $(1 - {x^2})dy + xydx = x{y^2}dx$ is

Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is

If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $

$\int_{}^{} {{e^{2x}}\left( {\frac{{\sin 4x - 2}}{{1 - \cos 4x}}} \right)\;dx = } $

Distance between the two parallel lines $y = 2x + 7$and $y = 2x + 5$ is

$n$ balls each of weight $w$ when weighted in pairs the sum of the weights of all the possible pairs is $120$ when they are weighed in triplets the sum of the weights comes out to be $480$ for all possible triplets, then $n$ is

The value of ${\log _3}\,4{\log _4}\,5{\log _5}\,6{\log _6}\,7{\log _7}\,8{\log _8}\,9$ is

For the ellipse $25{x^2} + 9{y^2} - 150x - 90y + 225 = 0$ the eccentricity $e = $