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 $x=0$

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