The function f(x) = 2x + 3x(2)/(3), x ∈ R , has

Given: $f ( x ) = 2x + 3 ( x) \dfrac{2}{3}$

$⇒ {f}^{'}\left(x\right) = 2 + 2x\dfrac{- 1}{3}$

$⇒ {f}^{'}\left(x\right) = 2\left(1 + \dfrac{1}{x\dfrac{1}{3}}\right)$

$⇒ {f}^{'}\left(x\right) = 2\left(\dfrac{x\dfrac{1}{3} + 1}{x\dfrac{1}{3}}\right)$

The function changes from positive to negative at $x = 1$ and from negative to positive at $x = 0$

So, the point of local maxima \left(M\right)$is at$x = - 1$and the point of local minima \left(m\right)$ at $x = 0$