list the critical numbers of the following function in increasing order. enter n in any blank that you dont…

Explanation:

Step1: Find the derivative

Use the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$. $g'(x)=6\times\frac{1}{3}x^{\frac{1}{3}-1}-6\times(-\frac{2}{3})x^{-\frac{2}{3}-1}=2x^{-\frac{2}{3}} + 4x^{-\frac{5}{3}}=\frac{2}{x^{\frac{2}{3}}}+\frac{4}{x^{\frac{5}{3}}}=\frac{2x + 4}{x^{\frac{5}{3}}}$

Step2: Set the derivative equal to zero

Set $g'(x)=0$, then $\frac{2x + 4}{x^{\frac{5}{3}}}=0$. A fraction is zero when the numerator is zero and the denominator is non - zero. $2x+4 = 0$ gives $x=-2$.

Step3: Find where the derivative is undefined

The derivative $g'(x)=\frac{2x + 4}{x^{\frac{5}{3}}}$ is undefined when $x = 0$ (since the denominator $x^{\frac{5}{3}}=0$ when $x = 0$).

Answer:

-2, 0, N