g(x)=6x^1/3 + 3x^4/3
Identify intervals where the function is increasing/decreasing, concave up/down, critical numbers and inflection points??

Question

g(x)=6x^1/3 + 3x^4/3
Identify intervals where the function is increasing/decreasing, concave up/down, critical numbers and inflection points??

abb0t · Answer

Take the first derivative and the second derivative to find what you seek here. Can you do that ? Then, find the roots.

bmorse · Answer

I took the derivative and got critical numbers x=-1/2,0 but I'm not sure how to set it up to find where it is increasing and decreasing and so on...

anonymous · Answer

If you have a graphing calculator you could plug it in and observe that way ...

bmorse · Answer

there are steps to take and answer using the derivatives...I just don't know exactly how to apply them in this specific case.

anonymous · Answer

$$g(x)=6x^{\frac{1}{3} }+ 3x^\frac{4}{3}$$
$$g'(x)=2x^{-\frac{2}{3}}+4x^{\frac{1}{3}}$$
you can do nothing with this until you get rid of the exponents and write what it really is

anonymous · Answer

$$g'(x)=\frac{2}{\sqrt[3]{x^2}}+4\sqrt[3]{x}$$

anonymous · Answer

add them up