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

MCQ

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

Correct option: C.

exactly one point of local maxima and exactly one point of local minima

c
$ 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) $

$ +\frac{1}{+}-\mathrm{m}^{-1}$

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

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