Graphing a cubed root function

[frosty8688]

1. Graph the following function



2. $\sqrt[3]{(x^{2}-1)^{2}}$



3. I got the first derivative to be $\frac{4x}{3\sqrt[3]{x^{2}-1}}$ but am having trouble with the second derivative to get the concavity. So far I have $\frac{4*3\sqrt[3]{x^{2}-1}-4x*3*\frac{1}{3\sqrt[3]{x^{2}-1}}}{9\sqrt[3]{(x^{2}-1)^{2}}}$

 

[SammyS]

1. Graph the following function

2. $\sqrt[3]{(x^{2}-1)^{2}}$

3. I got the first derivative to be $\displaystyle \frac{4x}{3\sqrt[3]{x^{2}-1}}$ but am having trouble with the second derivative to get the concavity. So far I have $\displaystyle \frac{4*3\sqrt[3]{x^{2}-1}-4x*3*\frac{1}{3\sqrt[3]{x^{2}-1}}}{9\sqrt[3]{(x^{2}-1)^{2}}}$

There appears to be an error in your second derivative.

What's the derivative of $\displaystyle 3\sqrt[3]{x^{2}-1}\ ?$