# How do you find the critical points for f(x)= x^(4/3) + 4x^(1/3)+ 4x^(-2/3)?

The critical points are $\left(1 , f \left(1\right)\right) = \left(1 , 9\right)$

#### Explanation:

First the domain of f(x) is $D \left(f\right) = \left(0 , + \infty\right)$ hence

we must find the roots of the first derivative which is

$\frac{\mathrm{df} \left(x\right)}{\mathrm{dx}} = \frac{4 \cdot \left({x}^{2} + x - 2\right)}{3 {x}^{\frac{5}{3}}}$

The roots of the derivative are the roots of the equation ${x}^{2} + x - 2 = 0$ hence $x = - 2$ , $x = 1$.

But $x = - 2$ does mot belong in the domain of f(x).